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  • ...tiplication]] operations can be [[simplify (mathematics)|simplified]] to a linear combination of distinct vectors. Linear combinations are for this reason often used as ...e space with the property that every vector can be uniquely expressed as a linear combination of the basis vectors. A [[linear transformation]] can be defined briefly a
    911 bytes (137 words) - 22:56, 25 November 2008
  • 177 bytes (27 words) - 09:33, 4 September 2009
  • 117 bytes (13 words) - 23:00, 25 November 2008

Page text matches

  • ...tiplication]] operations can be [[simplify (mathematics)|simplified]] to a linear combination of distinct vectors. Linear combinations are for this reason often used as ...e space with the property that every vector can be uniquely expressed as a linear combination of the basis vectors. A [[linear transformation]] can be defined briefly a
    911 bytes (137 words) - 22:56, 25 November 2008
  • ...r free module, and such that no element of the set can be represented as a linear combination of the others.
    245 bytes (42 words) - 06:20, 4 September 2009
  • {{r|linear combination}}
    492 bytes (60 words) - 15:09, 28 July 2009
  • Functions used as atomic orbitals in the linear combination of atomic orbitals molecular orbital method.
    141 bytes (18 words) - 04:48, 29 April 2009
  • ...y of a system of elements of a module or vector space, that no non-trivial linear combination is zero.
    149 bytes (23 words) - 16:48, 6 January 2009
  • ...[[module (algebra)|module]] or [[vector space]] is the set of all finite [[linear combination]]s of that set: it may equivalently be defined as the [[intersection]] of a
    968 bytes (162 words) - 13:20, 7 February 2009
  • ...that every element of <math>M</math> can be written uniquely as a finite [[linear combination]] of elements of <math>A</math>. The module <math>M</math> is said to be f ...such that every element of the module can be uniquely written as a finite linear combination of elements of the module. An equivalent definition of a basis for a modul
    2 KB (371 words) - 00:36, 2 February 2009
  • ...(mathematics)|ring]] or of a [[vector space]], is one for which the only [[linear combination]] equal to zero is that for which all the coefficients are zero (the "trivi
    2 KB (307 words) - 16:08, 7 February 2009
  • ...that every vector in <math>V</math> can be written uniquely as a finite [[linear combination]] of vectors in the basis. One may think of the vectors in a basis as buil
    3 KB (464 words) - 19:45, 1 December 2008
  • ...receding it, 1037, is the gcd. Now we want to write the gcd, 1037, as a [[linear combination]] of the two numbers we started with, in which the coefficients ''x'' and ' This gives 1037 as a linear combination of the two numbers in square brackets, which were among the successive rema
    7 KB (962 words) - 12:05, 3 May 2016
  • as an integer linear combination of the numbers (''a'',''b'') = ''ra'' + ''sb'' (with integers ''r'' and '' Since every such linear combination is divisible by all divisors common to
    5 KB (797 words) - 04:57, 21 April 2010
  • {{Image|Euclidean plane.png|right|350px|Fig. 1. Linear combination of vectors by the parallelogram rule. Construction is known as "parallelog ...cal-align: 20%"><math>\overrightarrow{OR}</math></font> resulting from the linear combination of <font style = "vertical-align: 20%"><math>\overrightarrow{OP}</math></f
    4 KB (632 words) - 10:13, 6 January 2010
  • ...ath>\mathbb{Z}/2\mathbb{Z}</math>, increasing all of the coefficients of a linear combination by <math>2</math> will result in the same element of the group.
    7 KB (1,154 words) - 02:39, 16 May 2009
  • ...enerated by a subset ''A'' may also be obtained as the set of all finite [[linear combination]]s of elements of ''A''.
    2 KB (414 words) - 03:00, 14 February 2010
  • ...<math>a</math>. The '''[[polynomial|polynomials]]''' then are [[finite]] [[linear combination|linear combinations]] of the monomials and the constant functions.
    8 KB (1,289 words) - 13:46, 26 May 2009
  • Every complex number is the real linear combination of the '''real unit'''
    3 KB (468 words) - 17:28, 1 January 2010
  • ...according to the Pauli principle. This problem can be overcome by taking a linear combination of two orbital products ...accurate theories (such as [[configuration interaction]] and [[MCSCF]]), a linear combination of Slater determinants is needed.
    11 KB (1,582 words) - 07:52, 23 September 2009
  • ...n function that is "smeared out" over a whole molecule. Usually an MO is a linear combination of [[atomic orbital]]s (an LCAO), which is a weighted sum of (almost) all a ...araday Soc., vol '''25''', p. 668 (1929).</ref> introduced the following ''linear combination of atomic orbitals'' (LCAO) way of writing an MO &phi;:
    8 KB (1,408 words) - 09:47, 24 April 2010
  • In addition, a linear combination of these solutions is also a solution:
    3 KB (459 words) - 07:58, 13 July 2012
  • By a simple linear combination of solid harmonics of &plusmn;''m'' these functions are transformed into re ====Linear combination ====
    16 KB (2,612 words) - 09:02, 9 February 2010
  • ...monics a power of ''r''<sup>2</sup> cannot be factored out by forming some linear combination [since regular harmonics span an [[irreducible representation]] of the [[gr A contracted set is a predetermined linear combination of radial parts of GTOs (that are on the same center). Indexing different p
    15 KB (2,490 words) - 12:23, 19 April 2009
  • ...''a''<sub>1</sub>, ..., ''a''<sub>''p''</sub> not all zero, such that the linear combination is the zero vector in ''V'',
    15 KB (2,506 words) - 05:16, 11 May 2011
  • ...accounted for, and we can take it out of this space. The single remaining linear combination will belong to another eigenspace of '''J'''<sup>2</sup>. We can repeat this argument for the three products with ''M'' = 3. One linear combination of the three is already accounted for and can be removed, two linear combin
    21 KB (3,338 words) - 10:45, 11 June 2009
  • *see also [[Linear combination of atomic orbitals molecular orbital method]]
    14 KB (2,154 words) - 09:32, 12 November 2007
  • ...independent]], it follows that any vector in the plane can be written as a linear combination of these two non-collinear vectors. (This is also expressed as: Any vector
    16 KB (2,609 words) - 03:09, 8 March 2024
  • ...independent]], it follows that any vector in the plane can be written as a linear combination of these two non-collinear vectors. (This is also expressed as: Any vector
    16 KB (2,638 words) - 03:10, 8 March 2024
  • ...e of the system. In other words, the state of any system is reducible to a linear combination of solutions of the Schrödinger equation for that system. The Hamiltonian ...y exist in the system as defined, and so the particle's state must be some linear combination of the eigenstates of ''H''.
    17 KB (2,678 words) - 10:12, 9 May 2011
  • ...the same longitudinal vector. Hence, the three fields can be written as a linear combination of two orthonormal vectors, '''e'''<sub>''x''</sub> and '''e'''<sub>''y''</
    15 KB (2,576 words) - 00:07, 1 December 2010
  • It can be shown that the following linear combination is the only totally invariant function with ''ℓ'' = 4:
    15 KB (2,390 words) - 10:11, 5 February 2010
  • ...mponents of the same second rank tensor, a Lorentz transformation gives a linear combination of '''E''' and '''B''', and hence in relativity theory these two fields do
    5 KB (833 words) - 21:31, 26 March 2022
  • Any 2x2 Hermitian matrix may be written as a linear combination of the 2&times;2 identity matrix and the three [[Pauli spin matrices]]. The
    6 KB (1,000 words) - 10:33, 3 February 2011
  • ...m variables called '''factors'''. The observed variables are modeled as [[linear combination]]s of the factors, plus "[[errors and residuals in statistics|error]]" term ...r constant times their level of mathematical intelligence, i.e., it is a [[linear combination]] of those two "factors". The numbers, for this particular subject, by wh
    16 KB (2,339 words) - 19:24, 29 September 2020
  • into the linear combination
    18 KB (2,797 words) - 14:37, 30 January 2011
  • {{Image|Moving wave.gif|right||<small>Fig. 5. Linear combination of lowest 3 modes </small> }}
    17 KB (2,899 words) - 02:27, 24 March 2010
  • ...that the electron wavefunction in a crystal is made up of a [[LCAO method|linear combination of atomic orbitals]] with undetermined coefficients. Symmetry of the crysta
    7 KB (1,045 words) - 09:16, 9 April 2011
  • ...component of '''A''' is a vector perpendicular to '''k''' and hence is a linear combination of '''e'''<sup>(1)</sup> and '''e'''<sup>(&minus;1)</sup>. The superscript
    23 KB (3,635 words) - 12:14, 7 December 2009
  • ...''A''-th nucleus, then the MO &phi; of electron 1 has the following LCAO (linear combination of atomic orbitals) form,
    20 KB (3,082 words) - 17:39, 9 December 2008
  • ...pread out" over a molecule. Usually this is a consequence of an MO being a linear combination (weighted sum) of atomic orbitals centered on different atoms.
    10 KB (1,514 words) - 19:38, 20 November 2009
  • <math>\mathbf{r}_3</math>. Thus the latter two vectors are a linear combination of the first two,
    16 KB (2,502 words) - 12:28, 24 March 2010
  • 20 KB (3,194 words) - 03:34, 8 November 2013