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Matrix
A '''matrix''' (plural "matrices") is a mathematical construct generally represented as ...ormation]] can be represented by a [[uniqueness|unique]] matrix, and every matrix represents a unique linear transformation.

15 KB (2,209 words) - 02:10, 14 February 2010
Zero matrix
...ent]] for [[matrix multiplication]] and as the [[additive identity]] for [[matrix addition]]. It represents the zero [[linear map]]. ...may be denoted <math>\scriptstyle 0_{m,n}</math> for an ''m''×''n'' matrix, so (for example)

1 KB (172 words) - 16:40, 6 February 2009
Diagonal matrix
In [[matrix algebra]], a '''diagonal matrix''' is a [[square matrix]] for which only the entries on the main [[diagonal]] can be non-zero, and The [[matrix addition|sum]] and [[matrix multiplication|product]] of diagonal matrices are again diagonal, and the d

2 KB (230 words) - 02:39, 7 January 2009
Hermitian matrix
...x conjugate|complex conjugate]] of the corresponding entry in the original matrix: or in matrix notation:

6 KB (1,000 words) - 10:33, 3 February 2011
Matrix multiplication
#REDIRECT [[Matrix#Matrix multiplication]]

42 bytes (4 words) - 15:25, 12 December 2008
Matrix (mathematics)
#REDIRECT [[Matrix]]

20 bytes (2 words) - 02:08, 10 December 2008
Idempotent matrix
#REDIRECT [[Matrix#Idempotent Matrix]]

38 bytes (4 words) - 15:34, 12 December 2008
Tutte matrix
...ath>A</math> of a [[Graph (mathematics)|graph]] ''G'' = (''V'',''E'') is a matrix used to determine the existence of a [[perfect matching]]: that is, a set o ...tices ''V'' has 2''n'' elements then the Tutte matrix is a 2''n'' × 2''n'' matrix A with entries

2 KB (259 words) - 17:10, 28 October 2008
Inverse matrix
#REDIRECT [[Matrix inverse]]

28 bytes (3 words) - 02:13, 10 December 2008
Symmetric matrix
#REDIRECT [[Matrix#Symmetric matrix]]

37 bytes (4 words) - 02:20, 10 December 2008
Matrix/Approval

12 bytes (1 word) - 19:54, 7 October 2007
Sylvester matrix
#REDIRECT [[Resultant (algebra)#Sylvester matrix]]

50 bytes (5 words) - 16:34, 17 December 2008
Identity matrix
...cation]]. Its entries are those of the [[Kronecker delta]]. The identity matrix represents the [[identity function]] as a [[linear map|linear operator]] on The identity matrix is also known as '''unit matrix''' because it possesses many of the properties of the multiplicative unit o

1,020 bytes (136 words) - 10:39, 23 April 2009
Orthogonal matrix
#REDIRECT [[Matrix#Orthogonal matrix]]

38 bytes (4 words) - 02:32, 10 December 2008
Square matrix
#REDIRECT [[Matrix#Square matrices]]

36 bytes (4 words) - 14:38, 7 November 2008
Matrix minor

36 bytes (3 words) - 16:06, 10 December 2008
Matrix ring
#REDIRECT [[Matrix#Operations]]

31 bytes (3 words) - 07:39, 22 December 2008
Adjugate matrix

36 bytes (3 words) - 16:09, 10 December 2008
Matrix/Bibliography
* ''Basic Matrix Theory'', Leonard E. Fuller, Prentice-Hall, 1962 * ''Matrix Computations'', Gene H.Golub and Charles F. Van Loan, John Hopkins Universi

336 bytes (40 words) - 15:20, 14 November 2007
Scalar matrix
#REDIRECT [[Matrix#Scalar matrix]]

34 bytes (4 words) - 09:39, 22 December 2008
Zero matrix/Definition
A matrix consisting entirely of zero entries.

81 bytes (10 words) - 15:11, 11 December 2008
Jacobi matrix

22 bytes (2 words) - 08:33, 14 January 2009
Matrix inverse
In [[matrix algebra]], the '''inverse''' of a [[square matrix]] '''A''' is '''X''' if where '''I'''''n'' is the ''n''-by-''n'' [[identity matrix]]

1 KB (158 words) - 00:36, 18 April 2009
Rotation matrix
...matrix''' is synonymous with a 3×3 [[orthogonal matrix]], which is a matrix '''R''' satisfying ...the [[transposed matrix]] and '''R'''−1 is the [[inverse matrix| inverse]] of '''R'''.

22 KB (3,624 words) - 01:45, 26 October 2013
Unit matrix
#REDIRECT [[Identity matrix]]

29 bytes (3 words) - 17:27, 9 December 2008
Diagonalizable matrix
#REDIRECT [[Diagonal matrix#Diagonalizable matrix]]

51 bytes (5 words) - 16:29, 11 December 2008
Jacobian matrix

22 bytes (2 words) - 12:58, 17 June 2009
Invertible matrix
#REDIRECT [[Matrix inverse]]

28 bytes (3 words) - 17:38, 9 December 2008
Matrix addition
#REDIRECT [[Matrix#Matrix addition]]

36 bytes (4 words) - 15:24, 12 December 2008
Matrix/Definition

118 bytes (14 words) - 12:49, 14 June 2008
Wigner D-matrix
...ctions of the Hamiltonian of spherical and symmetric [[rigid rotor]]s. The matrix was introduced by [[E. Wigner]] in 1927<ref>E. Wigner, ''Einige Folgerungen === Definition Wigner D-matrix ===

11 KB (1,671 words) - 06:37, 1 November 2009
Matrix/Related Articles

896 bytes (141 words) - 14:11, 9 January 2013
Tutte matrix/Definition
A matrix used to determine the existence of a perfect matching in a graph: that is,

183 bytes (31 words) - 17:13, 28 October 2008
Zero matrix/Related Articles
Auto-populated based on [[Special:WhatLinksHere/Zero matrix]]. Needs checking by a human. {{r|Diagonal matrix}}

514 bytes (67 words) - 21:47, 11 January 2010
Skew-symmetric matrix
#REDIRECT [[Matrix#Antisymmetric matrix]]

41 bytes (4 words) - 07:37, 22 December 2008
Hermitian matrix/Approval

12 bytes (1 word) - 12:47, 3 November 2007
Matrix inverse/Definition
The equivalent of the [[reciprocal]] defined for certain [[matrix|matrices]].

113 bytes (13 words) - 15:39, 10 November 2008
Identity matrix/Definition
...h ones on the main diagonal and zeroes elsewhere: the identity element for matrix multiplication.

152 bytes (21 words) - 13:19, 5 December 2008
Diagonal matrix/Definition
A square matrix which has zero entries off the main diagonal.

97 bytes (14 words) - 15:25, 11 December 2008
Hermitian matrix/Definition
Matrix which equals its conjugate transpose matrix, that is, is self-adjoint.

114 bytes (14 words) - 08:43, 4 September 2009
Matrix inverse/Approval

12 bytes (1 word) - 13:13, 23 January 2008
Rotation matrix/Definition
...imes;3 proper (unit determinant) orthogonal (orthonormal rows and columns) matrix

122 bytes (14 words) - 03:42, 13 July 2009
Wigner D-matrix/Definition
matrix in an irreducible representation of the groups SU(2) and SO(3); quantum mec

155 bytes (19 words) - 09:20, 12 October 2008
Matrix inverse/Related Articles
Auto-populated based on [[Special:WhatLinksHere/Matrix inverse]]. Needs checking by a human. {{r|Matrix}}

498 bytes (63 words) - 18:22, 11 January 2010
Identity matrix/Related Articles
Auto-populated based on [[Special:WhatLinksHere/Identity matrix]]. Needs checking by a human. {{r|Diagonal matrix}}

965 bytes (124 words) - 17:23, 11 January 2010
Diagonal matrix/Related Articles
Auto-populated based on [[Special:WhatLinksHere/Diagonal matrix]]. Needs checking by a human. {{r|Identity matrix}}

550 bytes (71 words) - 15:57, 11 January 2010
Rotation matrix/Related Articles
Auto-populated based on [[Special:WhatLinksHere/Rotation matrix]]. Needs checking by a human. {{r|Identity matrix}}

631 bytes (81 words) - 20:07, 11 January 2010
Hermitian matrix/Related Articles
Auto-populated based on [[Special:WhatLinksHere/Hermitian matrix]]. Needs checking by a human. {{r|Matrix}}

585 bytes (74 words) - 17:10, 11 January 2010
Wigner D-matrix/Approval

12 bytes (1 word) - 23:12, 15 November 2007
Tutte matrix/Related Articles
Auto-populated based on [[Special:WhatLinksHere/Tutte matrix]]. Needs checking by a human.

430 bytes (56 words) - 21:08, 11 January 2010
Wigner D-matrix/Related Articles
Auto-populated based on [[Special:WhatLinksHere/Wigner D-matrix]]. Needs checking by a human.

572 bytes (74 words) - 21:40, 11 January 2010
Wigner's D-matrix
#REDIRECT [[Wigner D-matrix]]

29 bytes (3 words) - 06:54, 5 September 2007

Page text matches

Zero matrix
...ent]] for [[matrix multiplication]] and as the [[additive identity]] for [[matrix addition]]. It represents the zero [[linear map]]. ...may be denoted <math>\scriptstyle 0_{m,n}</math> for an ''m''×''n'' matrix, so (for example)

1 KB (172 words) - 16:40, 6 February 2009
Diagonalizable matrix
#REDIRECT [[Diagonal matrix#Diagonalizable matrix]]

51 bytes (5 words) - 16:29, 11 December 2008
Identity matrix
...cation]]. Its entries are those of the [[Kronecker delta]]. The identity matrix represents the [[identity function]] as a [[linear map|linear operator]] on The identity matrix is also known as '''unit matrix''' because it possesses many of the properties of the multiplicative unit o

1,020 bytes (136 words) - 10:39, 23 April 2009
Diagonal matrix
In [[matrix algebra]], a '''diagonal matrix''' is a [[square matrix]] for which only the entries on the main [[diagonal]] can be non-zero, and The [[matrix addition|sum]] and [[matrix multiplication|product]] of diagonal matrices are again diagonal, and the d

2 KB (230 words) - 02:39, 7 January 2009
Skew-symmetric matrix
#REDIRECT [[Matrix#Antisymmetric matrix]]

41 bytes (4 words) - 07:37, 22 December 2008
Symmetric matrix
#REDIRECT [[Matrix#Symmetric matrix]]

37 bytes (4 words) - 02:20, 10 December 2008
Matrix addition
#REDIRECT [[Matrix#Matrix addition]]

36 bytes (4 words) - 15:24, 12 December 2008
Scalar matrix
#REDIRECT [[Matrix#Scalar matrix]]

34 bytes (4 words) - 09:39, 22 December 2008
Orthogonal matrix
#REDIRECT [[Matrix#Orthogonal matrix]]

38 bytes (4 words) - 02:32, 10 December 2008
Matrix multiplication
#REDIRECT [[Matrix#Matrix multiplication]]

42 bytes (4 words) - 15:25, 12 December 2008
Idempotent matrix
#REDIRECT [[Matrix#Idempotent Matrix]]

38 bytes (4 words) - 15:34, 12 December 2008
Identity matrix/Definition
...h ones on the main diagonal and zeroes elsewhere: the identity element for matrix multiplication.

152 bytes (21 words) - 13:19, 5 December 2008
Hermitian matrix/Definition
Matrix which equals its conjugate transpose matrix, that is, is self-adjoint.

114 bytes (14 words) - 08:43, 4 September 2009
Stroma/Definition
...ixation and the organelles DNA; thylakoid membranes are surrounded by this matrix.

180 bytes (26 words) - 15:56, 17 May 2010
Identity matrix/Related Articles
Auto-populated based on [[Special:WhatLinksHere/Identity matrix]]. Needs checking by a human. {{r|Diagonal matrix}}

965 bytes (124 words) - 17:23, 11 January 2010
Matrix/Bibliography
* ''Basic Matrix Theory'', Leonard E. Fuller, Prentice-Hall, 1962 * ''Matrix Computations'', Gene H.Golub and Charles F. Van Loan, John Hopkins Universi

336 bytes (40 words) - 15:20, 14 November 2007
Matrix inverse
In [[matrix algebra]], the '''inverse''' of a [[square matrix]] '''A''' is '''X''' if where '''I'''''n'' is the ''n''-by-''n'' [[identity matrix]]

1 KB (158 words) - 00:36, 18 April 2009
Diagonal matrix/Related Articles
Auto-populated based on [[Special:WhatLinksHere/Diagonal matrix]]. Needs checking by a human. {{r|Identity matrix}}

550 bytes (71 words) - 15:57, 11 January 2010
Zero matrix/Related Articles
Auto-populated based on [[Special:WhatLinksHere/Zero matrix]]. Needs checking by a human. {{r|Diagonal matrix}}

514 bytes (67 words) - 21:47, 11 January 2010
Cofactor (mathematics)/Definition
...nent of a matrix computation of the determinant; a signed determinant of a matrix minor.

131 bytes (19 words) - 16:33, 10 December 2008
Linear algebra
...a broad range of topics, such as [[systems of linear equations]], [[matrix|matrix algebra]], and [[arrow]]s in [[Cartesian coordinates|Cartesian]] two-dimens ...x algebra]], [[eigenvalue]]s and [[eigenvector]]s, [[linear operators]], [[matrix representation]]s, and [[inner product]]s find broad application in [[scien

975 bytes (135 words) - 02:13, 3 September 2010
Moore determinant
...s automorphism]] applied to the first column, i.e., an ''m'' × ''n'' matrix ...indices ''i'' and ''j''. (Some authors use the [[transpose]] of the above matrix.)

1 KB (199 words) - 15:30, 7 December 2008
Characteristic polynomial
...f a [[square matrix]] is a polynomial which has the [[eigenvalue]]s of the matrix as roots. Let ''A'' be an ''n''×''n'' matrix. The characteristic polynomial of ''A'' is the determinant

911 bytes (131 words) - 22:35, 17 February 2009
Matrix (mathematics)
#REDIRECT [[Matrix]]

20 bytes (2 words) - 02:08, 10 December 2008
Matrices
#redirect [[matrix]]

20 bytes (2 words) - 07:05, 26 January 2009
Invertible matrix
#REDIRECT [[Matrix inverse]]

28 bytes (3 words) - 17:38, 9 December 2008
Matrix ring
#REDIRECT [[Matrix#Operations]]

31 bytes (3 words) - 07:39, 22 December 2008
Inverse matrix
#REDIRECT [[Matrix inverse]]

28 bytes (3 words) - 02:13, 10 December 2008
Unit matrix
#REDIRECT [[Identity matrix]]

29 bytes (3 words) - 17:27, 9 December 2008
Eigenvalue/Definition
...'A''' ''v'' = λ ''v''; the number λ is the eigenvalue of the matrix '''A''' belonging to the eigenvector ''v''.

217 bytes (33 words) - 02:56, 2 February 2009
Wigner's D-matrix
#REDIRECT [[Wigner D-matrix]]

29 bytes (3 words) - 06:54, 5 September 2007
Square matrix
#REDIRECT [[Matrix#Square matrices]]

36 bytes (4 words) - 14:38, 7 November 2008
Tutte matrix
...ath>A</math> of a [[Graph (mathematics)|graph]] ''G'' = (''V'',''E'') is a matrix used to determine the existence of a [[perfect matching]]: that is, a set o ...tices ''V'' has 2''n'' elements then the Tutte matrix is a 2''n'' × 2''n'' matrix A with entries

2 KB (259 words) - 17:10, 28 October 2008
Sylvester matrix
#REDIRECT [[Resultant (algebra)#Sylvester matrix]]

50 bytes (5 words) - 16:34, 17 December 2008
Zero matrix/Definition
A matrix consisting entirely of zero entries.

81 bytes (10 words) - 15:11, 11 December 2008
Identity element
...[[matrix multiplication]]; a [[zero matrix]] is the identity element for [[matrix addition]].

927 bytes (140 words) - 15:33, 8 December 2008
Eigenvalue/Related Articles
{{r|Diagonal matrix}} {{r|Identity matrix}}

949 bytes (118 words) - 16:12, 11 January 2010
Diagonal matrix/Definition
A square matrix which has zero entries off the main diagonal.

97 bytes (14 words) - 15:25, 11 December 2008
Minimal polynomial/Definition
The monic polynomial of least degree which a square matrix or endomorphism satisfies.

121 bytes (16 words) - 17:52, 11 December 2008
Identity (mathematics)
** The [[identity matrix]], the neutral element for [[matrix multiplication]].

591 bytes (78 words) - 12:52, 31 May 2009
Matrix inverse/Definition
The equivalent of the [[reciprocal]] defined for certain [[matrix|matrices]].

113 bytes (13 words) - 15:39, 10 November 2008
Pauli spin matrices/Related Articles
{{r|Hermitian matrix}} {{r|Identity matrix}}

496 bytes (64 words) - 19:24, 11 January 2010
MATLAB
...]] created by the [[MathWorks]]. MATLAB allows easy [[Matrix (mathematics)|matrix]] manipulation, implementation of algorithms, plotting of [[Function (mathe

1 KB (141 words) - 11:14, 2 August 2010
Continuant (mathematics)/Definition
...in generalized continued fractions and as the determinant of a tridiagonal matrix.

165 bytes (21 words) - 15:39, 28 October 2008
Rotation matrix/Definition
...imes;3 proper (unit determinant) orthogonal (orthonormal rows and columns) matrix

122 bytes (14 words) - 03:42, 13 July 2009
Characteristic polynomial/Definition
The polynomial attached to a square matrix or endomorphism det(A-XI)=0.

107 bytes (14 words) - 17:55, 11 December 2008
Cofactor (mathematics)
...''' is a component of a [[matrix (mathematics)|matrix]] computation of the matrix [[determinant]]. Let ''M'' be a [[square matrix]] of size ''n''. The (''i'',''j'') '''minor''' refers to the determinant o

3 KB (430 words) - 06:46, 23 November 2009
Wigner D-matrix/Definition
matrix in an irreducible representation of the groups SU(2) and SO(3); quantum mec

155 bytes (19 words) - 09:20, 12 October 2008
Matrix inverse/Related Articles
Auto-populated based on [[Special:WhatLinksHere/Matrix inverse]]. Needs checking by a human. {{r|Matrix}}

498 bytes (63 words) - 18:22, 11 January 2010
Hermitian matrix/Related Articles
Auto-populated based on [[Special:WhatLinksHere/Hermitian matrix]]. Needs checking by a human. {{r|Matrix}}

585 bytes (74 words) - 17:10, 11 January 2010
Linear map/Related Articles
{{r|Identity matrix}} {{r|Zero matrix}}

559 bytes (73 words) - 18:06, 11 January 2010
Addiction/Catalogs
==Treatment modality matrix for addictions== !colspan=3|'''Treatment Modality Matrix'''

2 KB (174 words) - 00:25, 20 September 2009
Vector space/Related Articles
{{r|matrix representation}} {{r|matrix (mathematics)}}

492 bytes (60 words) - 15:09, 28 July 2009
Permanent/Definition
<noinclude>{{Subpages}}</noinclude>An invariant of a matrix consisting of the sum of all possible products taken one from each row and

142 bytes (23 words) - 13:32, 9 January 2013
Gaussian elimination/Related Articles
{{r|matrix}} {{r|matrix addition}}

579 bytes (84 words) - 14:09, 10 May 2009
Kronecker delta/Related Articles
{{r|Identity matrix}} {{r|Rotation matrix}}

721 bytes (92 words) - 17:54, 11 January 2010
Algebra over a field
...entries in ''F'' is an ''F''-algebra, with ''F'' embedded as the [[scalar matrix|scalar matrices]].

1 KB (155 words) - 15:55, 23 December 2008
Rotation matrix/Related Articles
Auto-populated based on [[Special:WhatLinksHere/Rotation matrix]]. Needs checking by a human. {{r|Identity matrix}}

631 bytes (81 words) - 20:07, 11 January 2010
Jacobian/Definition
Determinant of the matrix whose ith row lists all the first-order partial derivatives of the function

160 bytes (23 words) - 09:07, 4 September 2009
Resultant (algebra)
==Sylvester matrix== ...x''' attached to ''f'' and ''g'' is the square (''m''+''n'')×(''m''+''n'') matrix

2 KB (388 words) - 17:58, 21 December 2008
Fibonacci polynomials
:<math>F_n(x)=\left\{\begin{matrix} \end{matrix}\right.</math>

694 bytes (111 words) - 17:51, 21 January 2008
Hermitian matrix
...x conjugate|complex conjugate]] of the corresponding entry in the original matrix: or in matrix notation:

6 KB (1,000 words) - 10:33, 3 February 2011
Tutte matrix/Definition
A matrix used to determine the existence of a perfect matching in a graph: that is,

183 bytes (31 words) - 17:13, 28 October 2008
Character (group theory)
...[matrix]] group, is the [[trace (mathematics)|trace]] of the corresponding matrix.

680 bytes (98 words) - 06:19, 15 June 2009
Adhesion plaques
...membrane]] that anchor the [[biological cell|cell]] to an [[extracellular matrix]].

166 bytes (22 words) - 06:28, 24 September 2007
Absorbing element
* The [[zero matrix]] is the absorbing element for [[matrix multiplication]].

726 bytes (112 words) - 15:21, 21 December 2008
Eigenvalue
In [[linear algebra]] an '''eigenvalue''' of a (square) [[matrix]] <math>A</math> is a number <math>\lambda</math> that satisfies the eigenv where det means the [[determinant]], <math>I</math> is the [[identity matrix]] of the same [[dimension]] as <math>A</math>,

4 KB (731 words) - 17:16, 11 December 2008
Adhesion plaques/Definition
...membrane]] that anchor the [[Biological cell|cell]] to an [[extracellular matrix]].

161 bytes (21 words) - 06:16, 21 September 2008
Kronecker delta
...n'' [[identity matrix]]. The invariance of this matrix under [[orthogonal matrix|orthogonal]] change of coordinate makes δ a rank two [[tensor]].

1 KB (209 words) - 07:59, 22 December 2008
Spherical polar coordinates/Related Articles
{{r|Diagonal matrix}} {{r|Identity matrix}}

1,006 bytes (129 words) - 20:33, 11 January 2010
Laplace expansion (potential)/Definition
An expansion by means of which the determinant of a matrix may be computed in terms of the determinants of all possible smaller square

207 bytes (32 words) - 03:28, 4 September 2009
Idempotent element
...corresponding to direct sum decompositions. For example, the [[idempotent matrix]] is an idempotent for [[matrix multiplication]] corresponding to the operation of projection onto the ''x'

1,007 bytes (146 words) - 16:14, 13 December 2008
Pseudo-Hadamard transform
== Matrix version == The transform can also be expressed as a matrix multiplication of a data vector by the appropriate member of a recursively-

2 KB (395 words) - 05:48, 8 April 2024
Permanent
In mathematics, the '''permanent''' of a [[matrix]] is the sum of all possible products of elements taken from distinct rows

267 bytes (37 words) - 14:06, 9 January 2013
Euler angles/Related Articles
{{r|Rotation matrix}} {{r|Wigner D-matrix}}

955 bytes (150 words) - 03:40, 13 July 2009
Trace (mathematics)/Definition
Sum of diagonal elements of matrix; for linear operator ''T'', the trace is ''Σk'' &lang;''v<

240 bytes (45 words) - 06:17, 15 June 2009
2008 United States presidential election/External Links
...m/| The Next Government] - candidate profiles, issue areas, candidate idea matrix; provided by the Fels Center of Government, University of Pennsylvania

501 bytes (63 words) - 00:39, 15 September 2013
Connective tissue/Definition
...[[connective tissue cells]] embedded in a large amount of [[extracellular matrix]]<noinclude>{{DefMeSH}}</noinclude>

378 bytes (45 words) - 15:05, 1 July 2010
Minimal polynomial
...t object satisfies. Examples include the minimal polynomial of a [[square matrix]], an [[endomorphism]] of a [[vector space]] or an [[algebraic number]]. ==Minimal polynomial of a square matrix==

4 KB (613 words) - 02:34, 4 January 2013
Dyadic product
...to [[dot product]] and [[cross product]]. The dyadic product is a square [[matrix]] that represents a tensor with respect to the same system of axes as to wh ...duct of two matrices, the first being a column matrix and the second a row matrix,

3 KB (650 words) - 08:22, 2 December 2009
Quark
...ressed as a 3x3 unitary matrix, called the Cabibbo-Kobayashi-Maskawa (CKM) matrix, shown here in with the standard elements and the Wolfenstein parameterizat :<math>V=\left(\begin{matrix} V_{ud} & V_{us} & V_{ub} \\

3 KB (489 words) - 07:22, 28 May 2022
Pascal's Wager
One can put this into a decision matrix, as in [[game theory]]: |+ Pascal's Wager decision matrix

2 KB (425 words) - 09:51, 2 May 2010
Vector rotation
...d individually, a more economical method is to calculate a single rotation matrix for the entire tank and apply that solution to every current position of th ...ed, and this method has devoted followers and critics. Although several 3D matrix rotation methods can be used, the method of Hughes (J. Graphics Tools, 2000

4 KB (645 words) - 08:16, 22 April 2023
Cornel West
...o "ordinary people" - he has appeared in ''The Matrix Reloaded'' and ''The Matrix Revolutions'' as "Councilor West". He has also been involved in a number of

1 KB (183 words) - 20:45, 28 December 2020
Srivastava code
...) of length ''n'' is defined by a parity check matrix ''H'' of [[alternant matrix|alternant]] form

1 KB (155 words) - 15:31, 29 October 2008
Gaussian elimination
...e accomplished using written equations, but is more often simplified using matrix forms of the equations. == Matrix format ==

4 KB (574 words) - 05:42, 11 May 2009
Erlang (programming language)/Tutorials/erlangOOP
Its parent matrix, knows how to take the square root of a diagonal matrix. ...omplex number is a (subset of) complex matrices, if we think of a (1 by 1) matrix as a single number.

9 KB (1,125 words) - 07:07, 8 August 2009
Alternant code
...) of length ''n'' is defined by a parity check matrix ''H'' of [[alternant matrix|alternant]] form ''H''''i'',''j'' = αji''

1 KB (178 words) - 15:15, 29 October 2008
Matrix
A '''matrix''' (plural "matrices") is a mathematical construct generally represented as ...ormation]] can be represented by a [[uniqueness|unique]] matrix, and every matrix represents a unique linear transformation.

15 KB (2,209 words) - 02:10, 14 February 2010
Adjoint (disambiguation)
* [[Adjoint (linear algebra)]], the adjoint of a square matrix

251 bytes (38 words) - 12:40, 31 May 2009
Fuzzy control
* [[Fuzzy associative matrix]]

472 bytes (59 words) - 23:34, 14 February 2010
Cytoskeleton/Related Articles
{{r|Extracellular matrix}}

336 bytes (40 words) - 17:53, 29 July 2009
Population ecology/Related Articles
{{r|Leslie matrix}} {{r|Matrix population models}}

2 KB (240 words) - 10:16, 19 September 2008
Self-adjoint operator
...a matrix which is its own transpose) or a [[Hermitian matrix]] in (i.e., a matrix which is its own Hermitian transpose) when these matrices are viewed as (bo ...n case, all eigenvalues of a real symmetric matrix and a complex Hermitian matrix are real.

4 KB (709 words) - 06:58, 23 December 2008
V (disambiguation)
...]] was a movie produced in the early 21st century by the creators of [[The Matrix]] movie series.

393 bytes (65 words) - 12:44, 31 May 2009
Formal fuzzy logic/Related Articles
{{r|Fuzzy associative matrix}}

306 bytes (40 words) - 06:01, 10 September 2009
Circuit switching/Related Articles
{{r|Matrix switch}}

350 bytes (41 words) - 07:06, 26 January 2009
Euler's theorem (rotation)
.../font> these operators correspond one-to-one with orthogonal 3 × 3 [[matrix|matrices]] with determinant +1. Since for such (non-identity) matrices exa ...being [[associative product|associative]] and the inverse of an orthogonal matrix being orthogonal, the matrices form a [[group]] of infinite order, commonly

12 KB (1,865 words) - 02:49, 19 April 2010
Jacobian
In [[mathematics]], the '''Jacobi matrix''' is the matrix of first-order [[partial derivative]]s of the (vector-valued) function: ...Jacobi matrix for ''n'' = ''m'' is known as the '''Jacobian'''. The Jacobi matrix and its determinant have several uses in mathematics:

8 KB (1,229 words) - 08:32, 14 January 2009
Angiotensin receptor
...contractility, central [[osmoregulation|osmocontrol]] and [[extracellular matrix]] formation. ...of [[cell growth]], fetal tissue development, modulation of extracellular matrix, [[neuron]]al regeneration, [[apoptosis]], [[cellular differentiation]] and

3 KB (321 words) - 13:33, 15 June 2008
Erlang (programming language)/Tutorials/Simplify
looks nicer. In a matrix, we prefer the integers when possible, so we construct types of arguments, integer, float, imaginary, complex and matrix.

3 KB (332 words) - 07:07, 8 August 2009
Linear equation/Advanced
=== Linear matrix equations ===

3 KB (418 words) - 14:53, 4 March 2009
Continuant (mathematics)
...eneralized continued fraction]]s and as the determinant of a [[tridiagonal matrix]]. The extended continuant is precisely the determinant of the tridiagonal matrix

2 KB (293 words) - 17:21, 13 January 2013
Reflection (geometry)/Related Articles
{{r|Identity matrix}}

442 bytes (56 words) - 19:57, 11 January 2010
Tutte matrix/Related Articles
Auto-populated based on [[Special:WhatLinksHere/Tutte matrix]]. Needs checking by a human.

430 bytes (56 words) - 21:08, 11 January 2010
Congruence (disambiguation)
* In [[matrix theory]], the property of matrices relating to the same [[bilinear form]] w

645 bytes (93 words) - 12:51, 31 May 2009
Observable (quantum computation)
...it (notated by angular brackets) may not be one of the eigenvalues of the matrix.

3 KB (562 words) - 00:00, 17 February 2010
Spherical harmonics/Related Articles
*[[Wigner D-matrix]]

631 bytes (84 words) - 06:48, 31 January 2009
Linear quadratic control/Related Articles
{{r|Identity matrix}}

471 bytes (60 words) - 18:06, 11 January 2010
Stark effect/Related Articles
{{r|Wigner D-matrix}}

517 bytes (67 words) - 20:35, 11 January 2010
Wigner D-matrix
...ctions of the Hamiltonian of spherical and symmetric [[rigid rotor]]s. The matrix was introduced by [[E. Wigner]] in 1927<ref>E. Wigner, ''Einige Folgerungen === Definition Wigner D-matrix ===

11 KB (1,671 words) - 06:37, 1 November 2009
Cofactor (mathematics)/Related Articles
{{r|Matrix inverse}}

504 bytes (63 words) - 11:58, 11 January 2010
Monoid
...rices]] under [[matrix multiplication]] form a monoid, with the [[identity matrix]] as the identity element: this monoid is not in general commutative.

3 KB (526 words) - 11:02, 23 December 2008
Eckart conditions/Related Articles
{{r|Diagonal matrix}}

552 bytes (70 words) - 16:10, 11 January 2010
Dyadic product/Related Articles
{{r|Rotation matrix}}

508 bytes (65 words) - 16:07, 11 January 2010
Wigner D-matrix/Related Articles
Auto-populated based on [[Special:WhatLinksHere/Wigner D-matrix]]. Needs checking by a human.

572 bytes (74 words) - 21:40, 11 January 2010
Minimal polynomial/Related Articles
{{r|Diagonal matrix}}

544 bytes (70 words) - 18:34, 11 January 2010
Albert algebra
where <math>\cdot</math> denotes matrix multiplication.

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Slater determinant/Related Articles
{{r|Wigner D-matrix}}

641 bytes (79 words) - 20:25, 11 January 2010
Characteristic polynomial/Related Articles
{{r|Identity matrix}}

553 bytes (67 words) - 11:46, 11 January 2010
Molecular Hamiltonian/Related Articles
{{r|Wigner D-matrix}}

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Molecular orbital theory/Related Articles
{{r|Identity matrix}}

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Affine space/Related Articles
{{r|Rotation matrix}}

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Trace (mathematics)
In [[mathematics]], a '''trace''' is a property of a [[matrix]] and of a [[linear operator]] on a [[vector space]]. The trace plays an im ==Definition and properties of matrix traces==

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Identity function/Related Articles
{{r|Identity matrix}}

568 bytes (70 words) - 17:23, 11 January 2010
Euclidean space
...i''} such that the [[overlap matrix]] is not equal to the [[identity matrix]], ...tensor is a function of position and cannot be transformed to an identity matrix by a global transformation, i.e., by a single transformation holding on t

9 KB (1,403 words) - 02:22, 14 October 2013
Trace (mathematics)/Related Articles
{{r|Rotation matrix}}

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Linear independence/Related Articles
{{r|Diagonal matrix}}

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Rigid rotor/Related Articles
{{r|Wigner D-matrix}}

748 bytes (97 words) - 20:03, 11 January 2010
Least common multiple/Student Level
\begin{matrix} \end{matrix}

6 KB (743 words) - 18:42, 2 July 2009
Reflection (geometry)
...80°, see [[Rotation matrix#Explicit expression of rotation matrix|rotation matrix]]. Sometimes it is convenient to write this as a matrix equation. Introducing the [[dyadic product]], we obtain

8 KB (1,366 words) - 09:12, 10 August 2009
Graph theory/Related Articles
{{r|Tutte matrix}}

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ARIA (cipher)
...network]]. The permutation multiplies a 128-bit vector by a 16x16 Boolean matrix to get another 128-bit vector.

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Commutativity/Related Articles
{{r|Matrix}}

858 bytes (112 words) - 15:35, 11 January 2010
Lie algebra/representation
...cation of the abstract [[Lie algebra]] to a simpler [[Lie algebra#Examples|matrix Lie algebra]]. ...of ''V'' is minimal, this is called the fundamental representation of the matrix Lie algebra.

4 KB (670 words) - 21:07, 22 December 2011
Semigroup
* [[Square matrix|Square matrices]] under [[matrix multiplication]] form a semigroup, not in general commutative.

3 KB (405 words) - 16:21, 13 November 2008
Cartesian coordinates/Related Articles
{{r|Rotation matrix}}

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Orthogonal array
...h>OA(4N,4N-1,2,2)</math>. You just need to remove a column of 1's from the matrix: |Adamar matrix||Orthogonal array

4 KB (571 words) - 12:50, 24 June 2008
Vector field/Related Articles
{{r|Identity matrix}}

849 bytes (109 words) - 21:28, 11 January 2010
Adjoint (operator theory)
...a generalization of the notion of the Hermitian conjugate of a complex [[matrix]] to linear operators on [[complex number|complex]] [[Hilbert space|Hilbert ...n operator. The crucial observation here is the following: for any complex matrix ''M'', its Hermitian tranpose, denoted by ''M''&lowast;, is the

5 KB (914 words) - 08:41, 17 October 2009
Euler angles/Code
C Determine Euler angles of the proper rotation matrix A. C--Check if matrix is orthogonal with unit determinant.

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Basalt
...rained. It may be porphyritic containing larger crystals in a fine-grained matrix, vesicular with gas bubbles, or frothy scoria. The oceanic crust is compose

838 bytes (125 words) - 19:45, 31 December 2020
Principal component analysis
...components ascertained by [[eigenanalysis]] of the data sets [[covariance matrix]]. The most important components are found along the dimensions with the l

953 bytes (142 words) - 16:52, 4 August 2010
Euler's theorem (rotation)/Related Articles
{{r|Rotation matrix}}

852 bytes (135 words) - 02:37, 22 July 2009
Slater determinant
\begin{matrix} \chi_1(\mathbf{x}_1) & \chi_2(\mathbf{x}_1) & \cdots & \chi_N(\mathbf{x}_1 \end{matrix}

11 KB (1,582 words) - 07:52, 23 September 2009
Scalar
...r real (if the space is real and 3-dimensional it is called a [[rotation matrix|rotation]]). The [[determinant]] of a unitary transformation is a complex and the matrix-matrix product is implied,

9 KB (1,373 words) - 06:21, 11 December 2009
Albert algebra/Related Articles
{{r|Self-adjoint matrix}}

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Pauli spin matrices
...itian matrices]] which form an orthogonal basis (along with the [[identity matrix]]) for the real [[Hilbert space]] of 2 × 2 Hermitian matric :<math>\begin{matrix}

7 KB (1,096 words) - 05:49, 17 October 2013
U.K. support for Iraq during the Iran-Iraq War/Related Articles
{{r|Matrix Churchill}}

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Two-port network
The relations between inputs and outputs usually are expressed in matrix notation. |<math>Z_{21} = \begin{matrix} {V_\mathrm{2} \over I_\mathrm{1} }\end{matrix} \Big|_{I_{2}=0} </math>

20 KB (3,085 words) - 10:38, 2 July 2011
Field (mathematics)/Related Articles
{{r|Matrix inverse}}

1 KB (146 words) - 16:32, 11 January 2010
Euler angles
...pherical polar angles, in consequence the (''m'', ''m''′) [[Wigner D-matrix]]-element carries the complex phase exp[''i''π(''m''−''m''′ Write <math>\mathbf{R}(\varphi, \hat{n})</math> for the [[rotation matrix]] that describes a rotation around the unit vector <math>\hat{n}</math> ove

16 KB (2,502 words) - 12:28, 24 March 2010
Biomechanics
*[[cell differentiation|differentiating cells]] along the [[extracellular matrix]] during [[embryonic development]],

1 KB (174 words) - 15:37, 3 December 2008
Comparative biology
...ishes, (m) [[Chlorurus microrhinos]], feeds on the [[epilithic]] [[alga]]l matrix of [[coral reef]]s, (n) [[Siphonognathus argyrophanes]], feeds on small inv

1 KB (142 words) - 16:06, 20 May 2010
GF method
...terms of the same internal coordinates. Solving the GF equations gives the matrix that transforms from the linearized internal coordinates to the normal coor ...an matrix|Hessian]] of ''V'') evaluated in the minimum is a force constant matrix '''F'''. In the ''harmonic approximation''—on which the method is bas

13 KB (1,996 words) - 10:52, 3 November 2021
Vector field
...3 [[matrix]] obeying '''A'''T'''A''' = '''E''' (the [[identity matrix]]), then rotation of the coordinate axes by '''A''' gives

5 KB (928 words) - 04:59, 9 December 2009
Ring (mathematics)/Related Articles
{{r|Diagonal matrix}}

1 KB (174 words) - 20:03, 11 January 2010
Abrasive wheel
...minium oxide, zirconia alumina, and silicon carbide that are embedded in a matrix called the bond. The bond not only holds the abrasive grains together but a

1 KB (171 words) - 05:39, 12 September 2013
Rotation matrix
...matrix''' is synonymous with a 3×3 [[orthogonal matrix]], which is a matrix '''R''' satisfying ...the [[transposed matrix]] and '''R'''−1 is the [[inverse matrix| inverse]] of '''R'''.

22 KB (3,624 words) - 01:45, 26 October 2013
Special function/Catalogs/Catalog
|<math>\begin{matrix}\frac{d}{dx}\end{matrix} \ln \Gamma(x)</math> |<math>\left(\begin{matrix}\frac{d}{dx}\end{matrix}\right)^{m+1} \ln \Gamma(x)</math>

8 KB (1,184 words) - 14:58, 8 December 2009
Computer algebra system
*matrix operations

1 KB (164 words) - 14:01, 18 January 2008
Brining
...he cell also denatures its [[protein]]s. The proteins coagulate, forming a matrix which traps water molecules and holds them during cooking. This prevents th

1 KB (191 words) - 13:39, 10 April 2024
Bra-ket notation
...for performing and describing the [[linear algebra]] used throughout the [[matrix mechanics]] formulation of [[quantum mechanics]]. which is guaranteed to be the case for the eigenvectors of a Hermitean matrix.

4 KB (690 words) - 12:51, 26 March 2011
Yogini
The yogini, having a female body that is a matrix for menstruation and childbirth transformation through an awakened mooladha

1 KB (204 words) - 20:32, 14 February 2010
Ljubljana
*[http://www.on-the-matrix.com/europe/svn_ljubljana.asp Europe on the Matrix: Ljubljana, Slovenia] — Photographs and information.

2 KB (327 words) - 11:23, 4 November 2007
Morris the Explainer
...i Brothers|Laurence and Andrew Wachowski]], in which the [[The Oracle (The Matrix)|Oracle's]] role as [[Mentor (storytelling)|mentor]] is also used for exten

5 KB (696 words) - 16:59, 3 July 2009
Quantum mechanics/Timelines
*[[Werner Heisenberg]] invents matrix mechanics ...rödinger]] formulates his wave function equation; proves equivalence with matrix

4 KB (522 words) - 10:02, 11 April 2008
APP/Function
...198 {{#if: extracellular matrix organization and biogenesis |extracellular matrix organization and biogenesis|GO:0030198 }}] 

11 KB (1,519 words) - 11:17, 11 May 2009
Mythbusters
...II: Attack of the Clones", "Galaxy Quest", "Terminator 3", "A.I." and the "Matrix" sequels.He teaches model making in the industrial design department of the ...Attack of the Clones, Starship Troopers, Galaxy Quest, T3, The Matrix, The Matrix Reloaded and Van Helsing.

5 KB (750 words) - 05:14, 29 July 2023
Velocity
:<math> E_{v} = \begin{matrix} \frac{1}{2} \end{matrix} mv^2 </math>

4 KB (723 words) - 00:50, 1 November 2009
Lie algebra
...a field '''k''' together with the [[commutator#Ring theory|commutator]] of matrix multiplication, i.e. <math>[A,B]=A\circ B -B\circ A</math>. A straightforw ...k, -Id in the upper right block, and 0 in the rest. A 2''n''×2''n'' matrix ''A'' is an infinitesimal symmetry of ''J'' if

12 KB (1,918 words) - 20:29, 22 December 2011
Discriminant of an algebraic number field
Since any two '''Z'''-bases are related by a [[unimodular matrix|unimodular]] change of basis, the discriminant is independent of the choice

1 KB (235 words) - 01:20, 18 February 2009
Hybrid-pi model
...Bigg |_{v_{ce}=0} = \begin{matrix}\frac {I_\mathrm{C}}{ V_\mathrm{T} }\end{matrix} </math> is the [[transconductance]] in [[Siemens (unit)|siemens]], evaluat :* <math>V_\mathrm{T} = \begin{matrix}\frac {kT}{ q}\end{matrix}</math> is the ''[[Boltzmann constant#Role in semiconductor physics: the th

13 KB (2,071 words) - 10:15, 1 July 2011
Ring (mathematics)
...olynomial]]s of one variable with real coefficients, or a ring of square [[matrix|matrices]] of a given dimension. ...n</math> [[matrix|matrices]] forms a ring under componentwise addition and matrix multiplication. This ring is not commutative if ''n''>1.

10 KB (1,667 words) - 13:47, 5 June 2011
Modular form
...nteger]]s, <math>\mathrm{SL}_2(\mathbf{Z}))</math>, consisting of 2 by 2 [[matrix|matrices]] with integer entries and [[determinant]] 1, is referred to as th

1 KB (235 words) - 19:47, 15 December 2010
Crystal field theory
...bation theory]] suffices. This means that one must set up the perturbation matrix '''V''' of ''V''oct on basis of the five d-orbitals, ...found). Nowadays, in the era of computers, it is easy to diagonalize this matrix numerically. In the days of Bethe this was not possible, so that he was for

15 KB (2,390 words) - 10:11, 5 February 2010
Affine space
...e basis of ''V'' into the other, hence it is a square regular (invertible) matrix. The real numbers ''t''''i'' are the affine coordinates of ''O' the boldface capital indicates an ''n'' × ''n'' matrix.

15 KB (2,366 words) - 09:09, 4 April 2010
Mitochondrion
...nter-membrane space. The space enclosed within the inner membrane is the [[matrix]], a moderately dense region with strands of [[DNA]], [[ribosome]]s, or sma ...inter-membrane space is chemically like the [[cytosol]] while the internal matrix of the mitochondria contains a select set of molecules.<ref name=AlbertTheM

14 KB (2,053 words) - 19:41, 16 October 2014
Cellular respiration
Produces [[acetyl-CoA]] from pyruvate inside the mitochondrial matrix. This oxidation reaction also releases carbon dioxide as a product. In the ...sent, acetyl-CoA enters the [[citric acid cycle]] inside the mitochondrial matrix, and gets oxidised to [[CO2]] while at the same time reducing [[Nicotinamid

9 KB (1,309 words) - 04:08, 26 September 2007
Hazard and Operability Study
==Matrix of guide words and process parameters== Table 2 presents an example matrix of which typical guide words are applicable to each of a typical set of pro

14 KB (2,177 words) - 10:43, 8 April 2024
Ohm's law
...tensor is a real number σ0 times a 3×3 [[identity matrix]]. The scalar σ0 is the [[conductivity coefficient]] and

1 KB (225 words) - 02:06, 24 October 2009
Multiplication
...There are natural multiplication operations on the [[complex number]]s, [[matrix|matrices]], [[tensor]]s, [[sequence]]s, and [[function]]s. multiplication is not always commutative in other contexts. For example, [[matrix multiplication]] is in general not a commutative operation:

5 KB (638 words) - 14:16, 17 December 2008
Since I've Been Loving You/Catalogs
* 2000: Tequila & the Actual Matrix (''Radio Therapy'')

1 KB (175 words) - 07:53, 24 October 2009
Rayleigh-Ritz method
...ion into the functional at appropriate places, and using that the Hamilton matrix on basis of eigenvectors is diagonal with ''E''''k'' on the diag ===Matrix eigenvalue problem===

12 KB (1,893 words) - 04:51, 25 March 2010
Derivative at a point
...near map and hence may be represented by a [[matrix]]. The entries in the matrix are the [[partial derivative]]s of the component functions of ''F''''j

5 KB (861 words) - 14:04, 23 February 2011
Capital Asset Pricing Model
...ssets, meaning, that they all use the same expected returns and covariance matrix.

2 KB (242 words) - 20:23, 19 February 2010
YTCracker/External Links
...findarticles.com/p/articles/mi_m0HJE/is_2_1/ai_66012329 Suspicious Minds.] Matrix: The Magazine for Leaders in Education. 1 Sep 2000.

3 KB (352 words) - 01:18, 27 December 2013
Number theory/Signed Articles/Elementary diophantine approximations
== Matrix monoid <math>\mathit{SO}(\mathbb{Z}_+, 2)</math> == Obviously, the identity matrix

35 KB (5,836 words) - 08:40, 15 March 2021
Molecular orbital theory
...es decouple. The HF equations used then were in operator form—not in matrix form. ..., who wrote the HF equations in a basis of atomic orbitals, thus obtaining matrix equations. It is of course no coincidence that Roothaan performed this work

20 KB (3,082 words) - 17:39, 9 December 2008
Diabatic transformation
By applying the [[Leibniz rule]] for differentiation, the matrix elements of ''T''n are (where coordinates are suppressed for cl Assume that the off-diagonal matrix elements

13 KB (1,922 words) - 07:19, 7 May 2010
Levi-Civita tensor
{{cite book |title=Matrix Methods and Vector Spaces in Physics |author=Vinod K. Sharma |url=http://bo

2 KB (332 words) - 04:25, 12 October 2013
Adsorbent chemistries
...gend: P: Polymer matrix, S: Solute molecule, L: ligand attached to polymer matrix, H: Hydrophobic patch on solute surface, W: Water in bulk solution. Water ...ix]]. The strength of interaction between the [[solute]] molecule and the matrix is related to its [[ion|ionic strength]] and to the ability of the salt ion

17 KB (2,435 words) - 22:09, 18 December 2010
Atomic electron configuration
\begin{matrix} \end{matrix}

21 KB (3,868 words) - 09:15, 6 March 2024
Antisymmetrizer
where '''B''' is the matrix where the matrix '''S''', in [[quantum chemistry]] known as the ''overlap matrix'', is given by

15 KB (2,353 words) - 17:42, 9 December 2008
Linear quadratic control
...ying <math>Q,\Gamma \geq 0 </math> and <math>R</math> is a given symmetric matrix (of the corresponding size) satisfying <math>R > 0 </math>. In this setting where <math>P_k</math> is a real non-negative definite symmetric matrix satisfying the ''backward recursion'':

13 KB (2,418 words) - 05:46, 17 October 2013
Span of control
Matrix management is yet another complexity, where an individual may have a "home"

2 KB (338 words) - 13:33, 29 May 2009
Edward G. Jones
...n]] from [[layer V]] cortical neurons and the cells of the core and of the matrix of the dorsal thalamus, form a substrate for the synchronization of the dis ...d he was elected a member of the [[American Academy of Sciences]]. For his matrix-core theory of organization in consciousness and perception, he received th

5 KB (781 words) - 07:20, 28 March 2023
Cyberpunk
...behind "cyberpunk" peaked in the early to mid 1990s, movies such as [[The Matrix]] trilogy, [[Lawnmower Man]], and [[anime]] shows such as ".hack" have cont ...and the ideas involved (for example, the neural interface conveyed in the Matrix: the concept of "jacking in" through a direct link between the communicatio

5 KB (763 words) - 18:31, 13 March 2024
Curl
As a vector-matrix-vector product: where the matrix has the following components:

7 KB (1,067 words) - 07:27, 23 October 2021
Ellipse/Citable Version
:<math>\begin{matrix} \end{matrix}</math>

23 KB (3,849 words) - 06:03, 29 August 2013
Ellipse
:<math>\begin{matrix} \end{matrix}</math>

23 KB (3,852 words) - 20:27, 9 January 2021
Rigid motion
...hich preserve distance. Hence they may be represented by the [[orthogonal matrix]] group ''O''(''n''). The orientation preserving maps are those of [[deter

3 KB (392 words) - 14:42, 28 November 2008
Elliptic curve
<math>\left(\begin{matrix}a&b\\c&d\end{matrix}\right)\in SL_2(\mathbb{Z})</math> acts on the upper half plane via the [[m ...alf plane, such that for any <math>\gamma=\left(\begin{matrix}a&b\\c&d\end{matrix}\right)\in SL_2(\mathbb{Z})</math> we have

10 KB (1,637 words) - 16:03, 17 December 2008
Collaborative filtering
The table below represents a User-Item Rating matrix for 4 users and 4 movies. Movies 'A-Team' and 'Salt' have more or less simi ...t to a certain user. Top-N recommendation techniques analyze the user-item matrix to correlate different users or items and use them to compute the recommend

15 KB (2,211 words) - 06:47, 19 October 2013
Angular momentum (classical)
is in general not (a constant times) the [[identity matrix]], the two vectors, '''L''' and '''ω''', are in general not parallel, ...ime dependence of the position vectors of a rigid body has the following [[matrix]]-vector form

23 KB (3,890 words) - 10:45, 11 June 2009
Eckart conditions
...'''B''' relating the internal and external modes to the displacements. The matrix '''B''' may be partitioned in an internal (3''N''−6 x 3''N'') and an We define the matrix '''M''' by

20 KB (3,213 words) - 02:14, 23 February 2010
Cubic equation/Proofs
:<math>\begin{matrix} \end{matrix}</math>

8 KB (1,339 words) - 11:08, 15 September 2009
Spherical polar coordinates
By direct matrix multiplication the matrix expression for the spherical polar coordinates of <math>\scriptstyle \vec{ The Cartesian metric tensor is the [[identity matrix]] and hence in Cartesian coordinates,

27 KB (4,267 words) - 10:14, 8 April 2023
Cytoskeleton
microvilli]]), and participate in some cell-to-cell or cell-to-matrix junctions and in the [[transduction]] of signals. ...nd of the [[sarcomere]]s. They also participate in some cell-cell and cell-matrix junctions. Many intermediate filaments are made of [[vimentin]]s. Others, i

6 KB (861 words) - 10:22, 24 January 2011
Factor analysis
:<math>\begin{matrix}x_{1,i} & = & \mu_1 & + & \ell_{1,1}v_i & + & \ell_{1,2}m_i & + & \varepsil \end{matrix}</math>

16 KB (2,339 words) - 19:24, 29 September 2020
Lambert W function
...begin{matrix}\frac{8}{3}\end{matrix}x^4 + \begin{matrix}\frac{125}{24}\end{matrix}x^5 - \cdots</math>

14 KB (2,354 words) - 21:43, 25 September 2011
Rigid rotor
It is possible to write the Lagrangian in matrix form: ...r, which always can be chosen orthonormal, since the tensor is [[Symmetric matrix|symmetric]]. When the rotor possesses a symmetry-axis, it usually coincide

25 KB (3,876 words) - 03:13, 1 October 2013
Born-Oppenheimer approximation
is over electronic coordinates only. By definition, the matrix with general element ...thbb{H}_\mathrm{e}(\mathbf{R})</math> is diagonal and the nuclear Hamilton matrix is non-diagonal with the following off-diagonal (''vibronic coupling'') ter

20 KB (3,194 words) - 03:34, 8 November 2013
Erlang (programming language)/Tutorials/Linda Sieve
numbers in the matrix. If we are looking for the primes below io:format(" Loading ~w numbers into matrix (+N) \n ", [ Max ] ),

8 KB (1,075 words) - 06:07, 29 November 2013
Stark effect
...The first quantum mechanical treatment (in the framework of Heisenberg's [[matrix mechanics]]) was by Wolfgang Pauli<ref>W. Pauli, ''Über dass Wasserstoffsp ...theory the first-order energies are the eigenvalues of the ''g'' x ''g'' matrix with general element

13 KB (2,036 words) - 18:38, 10 February 2010
Fleiss' kappa
...nt. The Fleiss' kappa can be computed from the data [[Matrix (mathematics)|matrix]] (see example below) to show the degree of agreement between the psychiatr

7 KB (939 words) - 12:41, 26 September 2007
Schrödinger equation
===Relation to Heisenberg's matrix mechanics=== ...With such an expansion in hand, the Schrödinger equation can be recast in matrix form in a few steps. Substituting the expansion for the wavefunction into t

17 KB (2,678 words) - 10:12, 9 May 2011
Jahn-Teller effect
...are the eigenvalues of the ''f''μ×''f''μ matrix with general element In order to predict whether the matrix elements of ''V'' are vanishing, Jahn and Teller transformed the nuclear Ca

21 KB (3,426 words) - 23:58, 27 October 2013
Algebra
...humb|350px|[[Linear algebra]] lecture about [[determinant]]s and [[inverse matrix|inverse matrices]].]]--> ...hich the specific properties of [[vector space]]s are studied (including [[matrix (mathematics)|matrices]]);

18 KB (2,669 words) - 08:38, 17 April 2024
Vector product
where <math>\left|\cdot\right|</math> denotes the determinant of a matrix. This determinant must be evaluated along the first row, otherwise the equa This implies that '''n'''×'''r''' can be written as a matrix-vector product,

12 KB (1,961 words) - 13:04, 11 June 2009
Tretinoin
...the synthesis of collagen and fibrillin while decreasing the production of matrix metalloproteinase.

8 KB (1,264 words) - 09:46, 28 November 2013
EMS VCS3
...[analog synthesizer]]; that is, it had patchable [[routing]] using a small matrix panel. The player would insert metal pins in this panel and connect section

3 KB (477 words) - 07:46, 30 September 2013
Current mirror
...1 \right) \left(1 + \begin{matrix} \frac{V_\mathrm{CB}}{V_\mathrm{A}} \end{matrix} \right) </math>, ::<math> R_N =r_O = \begin{matrix} \frac {V_A + V_{CB}} {I_C} \end{matrix} </math>,

25 KB (4,187 words) - 10:12, 22 June 2011
Rational number
...mber, which is to say, an ordinary integer, and a [[rational matrix]] is a matrix whose coefficients are rational numbers. [[Rational polynomial]] usually, a

9 KB (1,446 words) - 08:52, 30 May 2009
Fatty acid metabolism
...[[acyl]] [[CoA]] is transported into the mitochondrial [[matrix (biology)|matrix]]. This occurs via a series of similar steps:

7 KB (1,029 words) - 16:31, 25 March 2010
Advanced Encryption Standard
The other two give diffusion, treating the 128-bit block as a four by four matrix of bytes (as did an earlier cipher from the same designers, [[Square (ciphe

3 KB (507 words) - 05:48, 8 April 2024
U.S. Intelligence and terrorism from 2000
====World-Wide Attack Matrix==== ...iefing held on September 15, 2001, where he presented the Worldwide Attack Matrix, a classified document describing covert CIA anti-terror operations in eigh

11 KB (1,546 words) - 04:39, 5 April 2024
Green's function
It is illuminating to make the analogy with matrix equations. Let <math>\mathbb{L}</math> and <math>\mathbb{G}</math> be ''n'' then the solution of a matrix-vector equation is

10 KB (1,681 words) - 12:22, 11 June 2009
Group (mathematics)/Catalogs
** [[Matrix groups]]; e.g the [[general linear group]], the [[special linear group]],

5 KB (819 words) - 10:52, 15 September 2009
Spent nuclear fuel
...use of a uranium/thorium based fuel (233U in a 232Th matrix). Also present as a minor actinide is 237Np, this neptunium isot

8 KB (1,357 words) - 12:52, 15 March 2024
Chloroplast
...y)|membranes]], the interior of the inner membrane containing a semiliquid matrix, called [[stroma]], suspending a system of membranes, called [[thylakoid]]s

4 KB (518 words) - 02:30, 7 March 2024
Pascal's triangle
...e following text, we will call it the "Bernoulli triangle", even if this [[matrix]] does not resemble a triangle anymore ! ...d <math>\scriptstyle -1</math>. This is another hint that this object is a matrix. Each term in this row obeys the addition rule and the row rule. Some calcu

32 KB (4,192 words) - 18:42, 3 March 2024
Clebsch-Gordan coefficients
...the vector spaces involved, and then CG coefficients constitute a unitary matrix.

11 KB (1,759 words) - 10:02, 2 August 2008
Group theory
...examples of non-commutative multiplication arises in [[linear algebra]]. [[Matrix multiplication]] is not commutative (the product AB is not the same as BA). ...of all n-by-n [[invertible matrix|invertible]] real matrices together with matrix multiplication is a group. This group is called the [[general linear group]

15 KB (2,535 words) - 20:29, 14 February 2010
Solid harmonics
Since the transformation is by a [[unitary matrix]] the normalization of the real and the complex solid harmonics is the same \begin{matrix}

16 KB (2,612 words) - 09:02, 9 February 2010
U.K. support for Iraq during the Iran-Iraq War
...lso rejected that Members of Parliament tried to bias the court trying the Matrix Churchill defendants. In particular, it singled out Attorney General Sir Ni ...rolled organizations in the U.K. and U.S. One established British company, Matrix Churchill was bought by Iraq, its British branch an important manufacturer

28 KB (4,219 words) - 18:47, 3 April 2024
Hund's rules
...rgy). If there is weak spin-orbit coupling it is useful to diagonalize the matrix of the corresponding spin-orbit operator within the ''L-S'' basis [consisti

4 KB (593 words) - 09:31, 25 October 2009
Spherical harmonics
...or example, a rotation by angle α about the ''z''-axis is described by the matrix: where the form following the arrow applies for very small angles α. The matrix ''Rz'' is called the ''generator'' of the ''z''-rotation. The fa

34 KB (5,282 words) - 14:21, 1 January 2011
Sine
...e the proof in long-hand notation and only indicate briefly the equivalent matrix form. The unit vectors and angles that play a role in the proof are depicte ...ression are equivalent to the multiplication of a row vector with a square matrix). Putting Eqs. (1) and (2) for '''e'''''x'' " in terms of t

19 KB (3,106 words) - 09:53, 10 October 2013
Radiochemistry
...ion of the wanted element ''and/or'' to allow the radioactivity due to the matrix elements to decay before the measurement of the radioactivity. ...enta and red respectively. In the first picture a sample containing black (matrix), green and blue atoms is obtained, the sample is processed to extract only

13 KB (2,007 words) - 09:16, 6 March 2024
Influenza A virus
enzyme for virus particle assembly. Matrix protein surrounds the nucleocapsid and is envelope and matrix is digested and lowering of the pH causes HA protein to transform in a

8 KB (1,273 words) - 11:16, 15 September 2013
Flat file database
...am really stored the data table as a relevant data structure ([[array]], [[matrix]], [[vector]] of records, complex [[object]]...). Research data commonly constitute an observation matrix, in which each row is an observation vector, containing a standardized set

10 KB (1,620 words) - 01:14, 7 June 2012
Moller-Plesset
...on of the [[Slater-Condon rules]] for the simplification of ''N''-electron matrix ...[[canonical virtual orbitals]]. (Canonical orbitals diagonalize the [[Fock matrix]]). The quantities ε''i'', ε''j'', &e

10 KB (1,419 words) - 20:40, 10 February 2010
Magnetic moment
...or example, a rotation by angle α about the ''z''-axis is described by the matrix: where the form following the arrow applies for very small angles α. The matrix ''Rz'' is called the ''generator'' of the ''z''-rotation. The fa

20 KB (3,045 words) - 11:21, 29 June 2011
Gaussian type orbitals
...armonics]] (normalized to unity) can be defined by the following [[unitary matrix]]/vector expression \begin{matrix}

15 KB (2,490 words) - 12:23, 19 April 2009
Systems engineering
...he appropriate methodology to address issues in any category sector of the matrix. where it is anticipated that the solution is likely to involve design of s

5 KB (675 words) - 10:50, 23 February 2024
Polarizability
...pha;''' is expressed with respect to the very same coordinate system by a matrix, ...basis the polarizibility '''α''' is represented by another 3×3 matrix. This means that '''α''' is a second rank (because there are two indi

12 KB (1,839 words) - 10:43, 5 October 2009
United States intelligence community
The matrix below is organized by intelligence disciplines. Some agencies collect infor

6 KB (811 words) - 07:37, 18 March 2024
Geotechnical engineering
...and the relative quantities of mineral, water and air present in the soil matrix. Fine particles (fines) are defined as particles less than 0.075 mm in diam ...'', which is the hydrostatic pressure of free water at a point in the soil matrix, is also important in soil mechanics.

15 KB (2,155 words) - 16:26, 3 April 2010
Tobacco
...smoke via the enhancement of inflammatory processes and the activation of matrix [[metalloproteases]].

5 KB (678 words) - 08:07, 30 September 2016

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