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• Norm
  ...f><ref group="Note">The other mistake books make is saying explicitly that the [[field of a vector space]] needs to be {{M|\mathbb{R} }}, it may commonly # <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
• Inner product
  {{:Inner product/Infobox}} ...here {{M|F}} is either {{M|\mathbb{R} }} or {{M|\mathbb{C} }}), an ''inner product''<ref>http://en.wikipedia.org/w/index.php?title=Inner_product_space&oldid=6
  6 KB (1,016 words) - 12:57, 19 February 2016
• Norm/Heading
  ...w\mathbb{R}_{\ge 0} }}</span><br/>Where {{M|V}} is a [[vector space]] over the [[field]] {{M|\mathbb{R} }} or {{M|\mathbb{C} }} * [[inner product space|inner product spaces]]
  1 KB (194 words) - 19:28, 25 January 2016
• Site projects:Patrolling topology/Task list
  * [[Quotient (topology)]] - '''DONE''' - [[User:Alec|Alec]] ([[User talk:Alec|talk]]) 15:55, 21 Ap * [[Topology]] - '''DONE''' [[User:Alec|Alec]] ([[User talk:Alec|talk]]) 20:50, 12 May 2
  4 KB (404 words) - 21:36, 30 September 2016
• The real numbers/Infobox
  |title=The real numbers |data2=Main page: [[The real line]]''
  1 KB (213 words) - 21:31, 26 February 2017
• Exercises:Saul - Algebraic Topology - 7/Exercise 7.6
  # Compute the singular homology groups of {{M|T^2:\eq\mathbb{S}^1\times\mathbb{S}^1}} and {{:Exercises:Saul - Algebraic Topology - 7/Exercise 7.6/X Complex}}
  10 KB (1,664 words) - 12:43, 1 March 2017
• Given a Hilbert space and a non-empty, closed and convex subset then for each point in the space there is a closest point in the subset
  ...{M|d:(x,y)\mapsto\Vert x,y\Vert}} where the [[norm is induced by the inner-product]], {{M|\Vert\cdot\Vert:x\mapsto\sqrt{\langle x,x\rangle} }} * If we both of have the following:
  3 KB (592 words) - 00:52, 7 April 2017
• For any vector subspace of a Hilbert space the orthogonal complement and the closure of that subspace form a direct sum of the entire space
  ...a [[Hilbert space]] and let {{M|L\subseteq X}} be a [[vector subspace]] of the [[vector space]] {{M|(X,\mathbb{K})}}, then{{rW2014LNFARS}}: ...the norm]] {{M|\Vert\cdot\Vert}} which is the [[norm induced by the inner product]] {{M|\langle\cdot,\cdot\rangle}}</ref>
  3 KB (633 words) - 04:07, 8 April 2017
• Orthogonal complement
  ...te">{{XXX|Can we relax this to a subset maybe?}}</ref>, then we may define the ''[[orthogonal vectors|orthogonal]] complement'' of {{M|L}}, denoted {{M|L^ ...le\eq 0}}]]{{M|]\ \Big\} }} - notice that {{M|\langle x,y\rangle\eq 0}} is the definition of {{M|x}} and {{M|y}} being ''[[orthogonal vectors]]'', thus:
  2 KB (278 words) - 04:07, 8 April 2017