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• Bilinear map
  ...inear map|linear map]] 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
  ...ote">The 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|\mathb # <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
• Cauchy-Schwarz inequality
  ...ighlight|Update: [[Cauchy-Schwarz inequality for inner product spaces]] is a proof of the second form - note that {{M|\Vert x\Vert:\eq\sqrt{\langle x,x\ ...he solutions (to <math>f(x)=0</math>) will at be: <math>x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}</math>
  3 KB (609 words) - 13:04, 4 April 2017
• Index of notation
  ...,\mathbb{R})</math> denotes the continuous function on the interval {{M|[a,b]}} that map to {{M|\mathbb{R} }} - this is unlikely to be given any other w | {{M|\mathbb{S}^n}}, {{M|l_2}}, {{M|\mathcal{C}[a,b]}}
  9 KB (1,490 words) - 06:13, 1 January 2017
• Span, linear independence, linear dependence, basis and dimension
  Given a set of vectors {{M|S}} in a vector space {{M|(V,F)}} A set {{M|E}} in a [[Vector space|vector space]] {{M|(V,F)}} is linearly dependent if for any
  2 KB (330 words) - 18:07, 25 April 2015
• Sequence
  A sequence is one of the earliest and easiest definitions encountered, but I ...prefer it. This notation is inline with that of a [[Tuple|tuple]] which is a generalisation of [[Ordered pair|an ordered pair]].
  2 KB (419 words) - 18:12, 13 March 2016
• Basis and coordinates
  This is very much a "motivation" page and a discussion of the topic. ==What is a coordinate==
  9 KB (1,525 words) - 16:30, 23 August 2015
• Formal logic language
  ...y so in set theory, but overall an important role. It is important to have a concrete understanding of this. *<math>\text{Plus}(\text{Natural }a,\text{Natural }b)\rightarrow\text{Natural}</math>
  2 KB (410 words) - 16:35, 9 March 2015
• Group
  {{Requires references|The bulk of this page was written when this was a 'note project' and was taken from books (even though I was already really f ...denotes the group's operation applied to the elements {{M|a\in G}} and {{M|b\in G}}.
  7 KB (1,332 words) - 07:17, 16 October 2016
• Cardinality
  Informally the cardinality of a set is the number of things in it. The cardinality of a set {{M|A}} is denoted <math>|A|</math>
  2 KB (327 words) - 10:25, 12 March 2015
• Algebra of sets
  : '''Note: ''' Every ''algebra of sets'' is a ''[[ring of sets]]'' (see below) An ''algebra of sets'' is a collection of sets, {{M|\mathcal{A} }} such that{{rMTH}}:
  3 KB (507 words) - 18:43, 1 April 2016
• Sigma-ring
  A '''Sigma-ring''' or <math>\sigma</math>-ring, is closely related to [[Ring A non-empty class of sets {{M|S}} is a {{sigma|ring}} if<ref>Measure Theory, p24 - Halmos - Graduate Texts in Math
  728 B (125 words) - 15:34, 13 March 2015
• Sigma-algebra
  ...: ''' A ''Sigma-algebra'' of sets, or {{sigma|algebra}} is very similar to a [[Sigma-ring|{{sigma|ring}}]] of sets. ...ts]] is to an [[algebra of sets]] as a [[sigma-ring|{{sigma|ring}}]] is to a ''{{sigma|algebra}}''
  8 KB (1,306 words) - 01:49, 19 March 2016
• Measure Theory
  <math>[[a,b))\in\mathcal{J}^n</math> means <math>[a_1,b_1)\times[a_2,b_2)\times\cdots\t We can clearly get a ring from this, but not a [[Sigma-ring|{{Sigma|ring}}]] as for example:
  4 KB (733 words) - 01:41, 28 March 2015
• Additive function
  ...function]] on a class of [[set|sets]], {{M|\mathcal{A} }}, {{M|f:\mathcal{A}\rightarrow\mathbb{R} }} is called ''additive'' or ''finitely additive'' if ...|1=A\cap B=\emptyset}} ([[pairwise disjoint]]) and {{M|A\udot B\in\mathcal{A} }} we have:
  6 KB (971 words) - 18:16, 20 March 2016
• Pre-measure
  ...ef> is a [[Measure|measure]] on an [[Algebra of sets|algebra]] rather than a [[Sigma-algebra|{{Sigma|algebra}}]], the properties are as follows: ...an algebra of sets (a system of subsets of {{M|X}}) and {{M|\mu_0:\mathcal{A}\rightarrow[0,+\infty]}} such that:
  5 KB (782 words) - 01:49, 26 July 2015
• Measure
  {{Stub page|Requires further expansion|grade=A}}{{Extra Maths}}{{:Measure/Infobox}} A (positive) ''measure'', {{M|\mu}} is a [[set function]] from a [[sigma-ring|{{sigma|ring}}]], {{M|\mathcal{R} }}, to the positive [[extend
  6 KB (941 words) - 14:39, 16 August 2016
• Lebesgue measure
  ...Rene L. Schilling</ref> that assigns every half-open rectangle <math>[\![a,b)\!)=[a_1,b_1)\times\cdots\times[a_n,b_n)\in\mathcal{J}</math> as follows: <math>\lambda^n\big([\![a,b)\!)\big)=\prod^n_{i=1}(b_i-a_i)</math>
  804 B (129 words) - 00:28, 20 December 2016
• Complement
  ...|X}} the complement of {{M|A}} (often denoted {{M|A^c}}, {{M|A'}} or {{M|C(A)}}) is given by: <math>A^c=\{x\in X|x\notin A\}=X-A</math>
  726 B (145 words) - 13:28, 18 March 2015
• Ring
  {{Refactor notice|grade=A|msg=Page was ancient, mostly written in May 2015}} Not to be confused with [[Ring of sets|rings of sets]] which are a topic of [[Algebra of sets|algebras of sets]] and thus [[Sigma-algebra|{{Si
  7 KB (1,248 words) - 05:02, 16 October 2016