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• Vector space
  A '''vector space''', also known as a '''linear space''', is an abstract [[mathematics|math ...bb{R}^3</math></font> that are relatively easy to visualize, we can make a vector space out of <font style = "vertical-align: 17%"><math>\mathbb{R}^n</math></font
  15 KB (2,506 words) - 05:16, 11 May 2011
• Vector space/Approval
  12 bytes (1 word) - 17:44, 15 November 2007
• Vector space/Definition
  120 bytes (19 words) - 12:33, 29 November 2008
• Vector space/Related Articles
  {{r|dimension (vector space)}}
  492 bytes (60 words) - 15:09, 28 July 2009
• Dimension (vector space)/Definition
  The number of elements in any basis for a vector space.
  91 bytes (14 words) - 02:26, 11 December 2008

Page text matches

• Vector (disambiguation)
  {{rpl|Vector space}}
  264 bytes (30 words) - 02:32, 25 September 2013
• Linear combination
  ...eason often used as a stand-in whenever one expressions and equations in a vector space. ...ily expressed through linear combinations. For instance, a [[basis]] of a vector space can be defined as a set of vectors in the space with the property that ever
  911 bytes (137 words) - 22:56, 25 November 2008
• Scalar product (disambiguation)
  * [[inner product]], a generalisation of the above in an abstract vector space.
  242 bytes (36 words) - 12:38, 31 May 2009
• Banach space/Related Articles
  {{r|Vector space}}
  423 bytes (60 words) - 15:14, 28 July 2009
• Space (mathematics)/Related Articles
  {{r|Vector space}}
  359 bytes (48 words) - 15:04, 28 July 2009
• Linear space
  #REDIRECT [[vector space]]
  26 bytes (3 words) - 08:06, 5 November 2008
• Norm (mathematics)
  In [[mathematics]], a '''norm''' is a function on a [[vector space]] that generalizes to vector spaces the notion of the distance from a point Let ''X'' be a vector space over some subfield ''F'' of the [[complex number|complex numbers]]. Then a
  880 bytes (157 words) - 22:28, 20 February 2010
• Vector space/Related Articles
  {{r|dimension (vector space)}}
  492 bytes (60 words) - 15:09, 28 July 2009
• Hilbert space
  ...ger picture]]) of a quantum mechanical system is postulated to be a unit [[vector space|vector]] (i.e., a vector of norm 1) in some Hilbert space, and physical qua
  2 KB (258 words) - 12:33, 4 January 2009
• Normed space
  In [[mathematics]], a '''normed space''' is a [[vector space]] that is endowed with a [[norm (mathematics)|norm]]. A [[completeness|comp ...hbb{R}^n</math>. This is the canonical example of a ''finite dimensional'' vector space; in fact ''all'' finite dimensional real normed spaces of dimension ''n'' a
  982 bytes (148 words) - 07:17, 3 December 2007
• Euclidean space/Related Articles
  {{r|Vector space}} {{r|Euclidean vector space}}
  338 bytes (42 words) - 19:08, 5 October 2009
• Inner product space/Definition
  A vector space that is endowed with an inner product and the corresponding norm.
  116 bytes (17 words) - 13:40, 4 January 2009
• Basis (linear algebra)
  In [[linear algebra]], a '''basis''' for a [[vector space]] <math>V</math> is a set of [[vector]]s in <math>V</math> such that every ...respect to a basis. Through this transformation, every finite dimensional vector space can be considered to be essentially "the same as" the space <math>\mathbb{R
  3 KB (464 words) - 19:45, 1 December 2008
• Dimension (vector space)/Definition
  The number of elements in any basis for a vector space.
  91 bytes (14 words) - 02:26, 11 December 2008
• Similar matrices/Definition
  Matrices that represent the same endomorphism of a vector space with respect to different bases.
  132 bytes (18 words) - 17:44, 25 November 2008
• Norm (mathematics)/Definition
  A function on a vector space that generalises the notion of the distance from a point of a Euclidean spa
  157 bytes (26 words) - 15:01, 4 January 2009
• Frame of reference (physics)/Bibliography
  ...books.google.com/books?id=ybwBqELAJDEC&pg=PA71 |chapter=Lecture 2: Tangent vector space |pages=pp. 71 ''ff'' |isbn=0824703855 |year=2001 |publisher=CRC Press}} A s
  399 bytes (52 words) - 18:07, 20 March 2011
• Basis (linear algebra)/Definition
  ...ctors that, in a linear combination, can represent every vector in a given vector space or free module, and such that no element of the set can be represented as a
  245 bytes (42 words) - 06:20, 4 September 2009
• Banach space/Definition
  A vector space endowed with a norm that is complete.
  88 bytes (13 words) - 16:25, 14 July 2008
• Lattice (geometry)/Definition
  A discrete subgroup of a real vector space.
  79 bytes (11 words) - 13:32, 29 November 2008
• Normed space/Definition
  A vector space that is endowed with a norm.
  80 bytes (12 words) - 10:18, 4 September 2009
• Inner product/Definition
  A bilinear or sesquilinear form on a vector space generalising the dot product in Euclidean spaces.
  135 bytes (19 words) - 15:24, 28 November 2008
• Lattice (geometry)
  In [[geometry]], a '''lattice''' is a discrete subgroup of a real [[vector space]].
  96 bytes (14 words) - 13:26, 1 February 2009
• Linear map
  ...linear operator''') is a [[Function (mathematics)|function]] between two [[Vector space|vector spaces]] that preserves the operations of vector addition and [[Scal The term ''linear transformation'' is especially used for linear maps from a vector space to itself ([[Endomorphism|endomorphisms]]).
  1 KB (196 words) - 17:24, 20 December 2007
• Tangent space/Definition
  Vector space of all tangent vectors at a given point of a differentiable manifold.
  119 bytes (17 words) - 20:19, 4 September 2009
• Vector (mathematics)
  ...be labeled as 'vectors'. Thus, a vector is defined as a member of ''any'' vector space. Typical vector spaces include the real line, the Euclidean plane or space, ...ace is that superimposed vectors are again elements of the vector space (a vector space is closed under vector addition).
  4 KB (632 words) - 10:13, 6 January 2010
• Pointed set
  ...ebraic structures such as a [[monoid]], [[group (mathematics)|group]] or [[vector space]] have a distinguished element, such as an [[identity element]], and [[morp ** [[Affine space]] versus [[vector space]];
  1 KB (168 words) - 12:06, 22 November 2008
• Inner product space
  ...It is also a [[normed space]] since an inner product induces a norm on the vector space on which it is defined. A [[completeness|complete]] inner product space is
  1 KB (204 words) - 14:38, 4 January 2009
• Lie algebra/Definition
  A ''Lie algebra'' is a vector space together with a skew-symmetric bilinear operation (the bracket) that fulfil
  170 bytes (23 words) - 09:27, 27 November 2011
• Linear independence/Definition
  The property 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
• Span (mathematics)/Definition
  The set of all finite linear combinations of a module over a ring or a vector space over a field.
  133 bytes (23 words) - 13:20, 6 January 2009
• Field (mathematics)/Related Articles
  {{r|Vector space}}
  1 KB (146 words) - 16:32, 11 January 2010
• Ordered pair/Related Articles
  {{r|Vector space}}
  592 bytes (77 words) - 19:15, 11 January 2010
• Tangent space
  ...nt space''' of a [[manifold_(geometry)|differentiable manifold]] M is a [[vector space]] at a point p on the manifold whose elements are the tangent vectors (or v ===Directional derivatives as a vector space===
  4 KB (676 words) - 00:52, 15 November 2007
• Minimal polynomial
  ...the minimal polynomial of a [[square matrix]], an [[endomorphism]] of a [[vector space]] or an [[algebraic number]]. ...y dependent]] since the matrix ring has dimension ''n''² as a [[vector space]] over ''F'', and so ''A'' satisfies some polynomial. Hence it makes sense
  4 KB (613 words) - 02:34, 4 January 2013
• Euclidean plane/Related Articles
  {{r|Vector space}}
  566 bytes (74 words) - 16:25, 11 January 2010
• Abstract algebra
  ...|groups]], [[ring (mathematics)|rings]], [[field (mathematics)|fields]], [[vector space]]s, and [[algebra over a field|algebras]].
  250 bytes (31 words) - 07:40, 27 July 2008
• Barycentric coordinates
  In an [[affine space]] or [[vector space]] of [[dimension (vector space)|dimension]] ''n'' we take ''n''+1 points <math>s_0, s_1, \ldots, s_n</math
  1 KB (187 words) - 03:54, 1 April 2010
• Dimension (mathematics)
  {{r|Dimension (vector space)}}
  291 bytes (35 words) - 12:54, 31 May 2009
• Basis (linear algebra)/Advanced
  ...is a [[division ring]], <math>M</math> is called a [[vector space/Advanced|vector space]]. While every nontrivial vector space has a basis, not every module over an arbitrary ring will have a basis. Th
  2 KB (371 words) - 00:36, 2 February 2009
• Algebra over a field
  ...further [[algebraic structure]] of [[multiplication]] compatible with the vector space structure.
  1 KB (155 words) - 15:55, 23 December 2008
• Function (mathematics)/Related Articles
  {{r|Vector space}}
  1 KB (172 words) - 15:25, 15 May 2011
• Basis (linear algebra)/Related Articles
  {{r|Vector space}}
  203 bytes (25 words) - 16:47, 6 January 2009
• Inner product
  ...duct]] in the Euclidean spaces. Among other things, the inner product on a vector space makes it possible to define the geometric operation of projection onto a [[ Let ''X'' be a vector space over a [[field|sub-field]] ''F'' of the [[complex number|complex numbers]].
  3 KB (511 words) - 00:25, 20 February 2010
• Standard (mathematics)
  ...or complex [[vector space]]s (or, more generally, in any ''d''-dimensional vector space ''K''^d over a field ''K'')
  1 KB (212 words) - 21:14, 9 September 2020
• Linear combination/Related Articles
  {{r|vector space}}
  117 bytes (13 words) - 23:00, 25 November 2008
• Noetherian module
  ** A finite-[[dimension (vector space)|dimensional]] [[vector space]] over a [[field (algebra)|field]] is a Northerian module.
  1 KB (213 words) - 17:17, 7 February 2009
• Rigid motion
  ...''n'' dimensions as an [[affine space]] built on a [[real number|real]] [[vector space]] '''R'''^''n'' then the translations are the maps of the form ...x this point, we find that these must be [[linear map]]s of the underlying vector space which preserve distance. Hence they may be represented by the [[orthogonal
  3 KB (392 words) - 14:42, 28 November 2008
• Dot product
  ...ct), but it is only defined and makes sense in general for this particular vector space. Both the dot product and the cross product are widely used in in the stud
  3 KB (575 words) - 12:41, 14 February 2011
• Bra-ket notation
  ...echanics in mind it can be employed more generally when working with any [[vector space]].
  4 KB (690 words) - 12:51, 26 March 2011