Solution of triangles - Revision history

86.72.75.104: Add external link to TriSph

2014-11-13T22:01:55Z

Add external link to TriSph

← Older revision		Revision as of 00:01, 14 November 2014
Line 1:		Line 1:
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en>LGB: /* Two sides and non-included angle given (SSA) */ important addition

2014-02-18T11:40:57Z

Two sides and non-included angle given (SSA): important addition

← Older revision		Revision as of 13:40, 18 February 2014
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	~~In mathematics, a nonempty subset ''S'' of a [[group (mathematics)\|group]] ''G'' is said to be '''symmetric''' if~~
	~~:<math>S=S^{-1}</math>~~
	~~where <math>S^{-1} = \{ x^{-1} : x \in S \}</math>. In other words, ''S'' is symmetric if <math>x^{-1} \in S</math> whenever <math>x \in S</math>.~~

	If ''S'' is a subset of a [[vector space]], then ''S'' is said to be symmetric if it is symmetric with respect to the additive group structure of the vector space; that is, if <math>S = -S = \{ -x : x \in S \}</math>.

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	* In ~~'''R'''~~, ~~examples~~ of ~~symmetric sets are intervals~~ of the ~~type~~ <~~math~~>(-k, k)<~~/math~~> ~~with~~ <~~math~~>k > 0<~~/math~~>, and ~~the sets '''Z'''~~ and ~~<math>\{~~ -1, ~~1 \}~~<~~/math~~>.
	* Any vector subspace in a vector space is a ~~symmetric set~~.
	* If ''S'' is any subset of a group, ~~then~~ <~~math~~>~~SS^{-1}~~<~~/math~~> and ~~<math>S^{-1}S</math> are symmetric sets~~.

	~~==References==~~
	*R. ~~Cristescu~~, ~~Topological vector spaces~~, ~~Noordhoff International Publishing~~, ~~1977~~.
	*W. ~~Rudin, Functional Analysis, McGraw-Hill Book Company, 1973.~~

	~~{{PlanetMath attribution\|id=4528\|title=symmetric set}}~~

	~~{{Functional Analysis}}~~

	[[~~Category~~:~~Set theory~~]]

	~~{{settheory~~-~~stub}}~~

en>LGB at 10:23, 8 January 2014

2014-01-08T10:23:03Z

← Older revision		Revision as of 12:23, 8 January 2014
Line 1:		Line 1:
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			:<math>S=S^{-1}</math>
			where <math>S^{-1} = \{ x^{-1} : x \in S \}</math>. In other words, ''S'' is symmetric if <math>x^{-1} \in S</math> whenever <math>x \in S</math>.

			If ''S'' is a subset of a [[vector space]], then ''S'' is said to be symmetric if it is symmetric with respect to the additive group structure of the vector space; that is, if <math>S = -S = \{ -x : x \in S \}</math>.

			==Examples==
			* In '''R''', examples of symmetric sets are intervals of the type <math>(-k, k)</math> with <math>k > 0</math>, and the sets '''Z''' and <math>\{ -1, 1 \}</math>.
			* Any vector subspace in a vector space is a symmetric set.
			* If ''S'' is any subset of a group, then <math>SS^{-1}</math> and <math>S^{-1}S</math> are symmetric sets.

			==References==
			*R. Cristescu, Topological vector spaces, Noordhoff International Publishing, 1977.
			*W. Rudin, Functional Analysis, McGraw-Hill Book Company, 1973.

			{{PlanetMath attribution\|id=4528\|title=symmetric set}}

			{{Functional Analysis}}

			[[Category:Set theory]]

			{{settheory-stub}}

en>LGB: Dead link replaced

2012-08-21T06:21:28Z

Dead link replaced

New page

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