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• Homomorphism
  ** [[Homomorphism (vector space)]] - {{AKA}}: [[linear map]] - instance of a [[module homomorphism]] * [[Notes:Homomorphism]] - a notes-grade page that may provide some insight.
  4 KB (532 words) - 22:04, 19 October 2016
• Vector space
  An introduction to the important concepts of vector spaces and linear algebra may be found on the [[Basis and coordinates]] pag A vector space {{M|V}} over a [[Field|field]] {{M|F}} is a non empty set {{M|V}} and the binary operations:
  2 KB (421 words) - 16:30, 23 August 2015
• Bilinear map
  ...p]] which takes a point in a vector space to a point in a different vector space) ...inear map, and an ''[[Inner product|inner product]]'' is a special case of a bilinear form.
  4 KB (682 words) - 15:44, 16 June 2015
• Norm
  ...other mistake books make is saying explicitly that the [[field of a vector space]] needs to be {{M|\mathbb{R} }}, it may commonly be {{M|\mathbb{R} }} but i # <math>\forall x,y\in V\ \|x+y\|\le\|x\|+\|y\|</math> - a form of the [[Triangle inequality|triangle inequality]]
  6 KB (1,026 words) - 20:33, 9 April 2017
• Index of notation
  ...{{M|\mathbb{R} }} - this is unlikely to be given any other way because "C" is for continuous. | {{M|\mathbb{S}^n}}, {{M|l_2}}, {{M|\mathcal{C}[a,b]}}
  9 KB (1,490 words) - 06:13, 1 January 2017
• Addition of vector spaces
  * See [[Notes:Vector space operations]] ...1,\cdots,V_n</math> which are [[Vector space|vector spaces]] over the same field {{M|F}}:<br/>
  4 KB (804 words) - 18:02, 18 March 2016
• Kernel
  ...ernel of {{M|f:X\rightarrow Y}} (where {{M|f}} is a [[Function|function]]) is defined as: ...imbued with the concept of identity<ref group="footnotes">Ambiguous for [[Field|fields]] as they have two identities.</ref> (this identity shall be denoted
  2 KB (376 words) - 19:53, 10 May 2015
• Canonical linear map
  {{Stub page|grade=A*|msg=Important for work, needs work anyway. Be sure to link ...anonical linear isomorphism between a one dimensional vector space and its field]]}}
  1 KB (240 words) - 05:54, 7 December 2016
• External direct sum
  ...ternal direct sum''' of {{M|1=(V_i)_{i=1}^n}}, which we'll call the vector space {{M|V}}, as follows: *:*: Given a <math>u,v\in V</math> we define <math>u+v=(u_1+v_1,u_2+v_2,\cdots,u_n+v_n)<
  3 KB (613 words) - 13:12, 9 June 2015
• Notes:Vector space operations
  ...s page for evidence of operations on [[Vector space|vector spaces]] - that is the definitions of these operations according to different authors | Quoting: We say {{M|S}} is the ''direct sum'' of {{M|U}} and {{M|W}} if <math>\forall s\in S</math> th
  3 KB (489 words) - 20:27, 1 June 2015
• Bilinear form
  This is a specialisation of a [[Bilinear map]] and a generalisation of [[Inner product]] ...(V,F)}} be a [[Vector space|vector space]] over a [[Field|field]] {{M|F}}, a mapping:
  2 KB (283 words) - 09:48, 9 June 2015
• Tensor product of vector spaces
  {{Stub page|grade=A*|msg=Demote once more of it is finished!}} ...cdots\times V_k)}} denote the [[free vector space generated by|free vector space]] on {{M|\prod_{i\eq 1}^kV_k}}. We define the (abstract) ''tensor product''
  2 KB (377 words) - 21:33, 22 December 2016
• Linear map/Definition
  ...V</math> (because [[Mathematicians are lazy|mathematicians are lazy]]), is a linear map if: Which is eqivalent to the following:
  725 B (136 words) - 10:34, 12 June 2015
• Bilinear map/Definition
  ...en Roman - Third Edition - Springer Graduate texts in Mathematics</ref> is a [[Function|function]]: ...|linear]] in both variables. Which is to say that the following "Axioms of a bilinear map" hold:
  886 B (170 words) - 09:57, 12 June 2015
• Inner product space
  ...e'' ({{AKA}} an ''i.p.s'' or a ''pre-[[Hilbert space|hilbert]] space'') is a<ref name="FA">Functional Analysis - George Bachman and Lawrence Narici</ref * [[Vector space]] (over the [[Field|field]] {{M|\mathbb{R} }} or {{M|\mathbb{C} }}, which we shall denote {{M|F}}) {{
  949 B (161 words) - 21:08, 11 July 2015
• Normed space
  See: [[Subtypes of topological spaces]] for a discussion of relationships of normed spaces. A ''normed space'' is a<ref name="FA">Functional Analysis - George Bachman and Lawrence Narici</ref
  813 B (129 words) - 22:13, 11 July 2015
• Multilinear map
  This is a generalisation of [[Linear map|linear maps]] and [[Bilinear map|bilinear ma ...{M|1=U_1,\cdots,U_k}} all over a [[Field|field]] {{M|F}} to another vector space {{M|(V,F)}}:
  1 KB (203 words) - 23:27, 31 July 2015
• Space of all k-linear maps
  ...ily {{M|U_1,\cdots,U_k}}, of [[Vector space|vector spaces]] over a [[Field|field]] {{M|F}} we denote<ref name="ML">Multilinear Algebra - Second Edition - W. ...maps]] with domain {{M|U_1\times\cdots\times U_k}} that map to any vector space (over {{M|F}})
  1 KB (256 words) - 00:08, 1 August 2015
• Field
  ...date with the rest of the site, especially such a core AA definition|grade=A}} ...tative]] and has [[Ring with unity|unity]] with more than one element is a field if:
  951 B (151 words) - 21:29, 19 April 2016
• Quotient vector space
  * A [[vector space]] {{M|(V,\mathbb{F})}} over a [[field]] {{M|\mathbb{F} }} and * A [[vector subspace]] {{M|W\subseteq V}}
  5 KB (879 words) - 23:09, 1 December 2016