Normal (mathematics) - Revision history

Vipul: /* In category theory */

2008-12-26T07:02:55Z

In category theory

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	{{:Normal epimorphism}}		{{:Normal epimorphism}}

			{{:Normal category}}

	===In probability/statistics===		===In probability/statistics===

Vipul at 20:29, 9 June 2008

2008-06-09T20:29:11Z

← Older revision		Revision as of 20:29, 9 June 2008
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	{{:Normal distribution}}		{{:Normal distribution}}

			===In axiomatic set theory===

			{{:Normal function}}

			{{:Normal measure}}
	===Others===		===Others===

	{{:Normal number}}		{{:Normal number}}

Vipul at 14:12, 9 June 2008

2008-06-09T14:12:47Z

← Older revision		Revision as of 14:12, 9 June 2008
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	{{:Normal operator}}		{{:Normal operator}}
	===In ~~Galois~~ theory===		===In field theory===

	{{:Normal field extension}}		{{:Normal field extension}}

Vipul at 14:11, 9 June 2008

2008-06-09T14:11:36Z

← Older revision		Revision as of 14:11, 9 June 2008
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	{{:Normal coordinate system}}		{{:Normal coordinate system}}

	===In ~~normed vector spaces~~===		===In category theory===

	~~In general normed vector spaces, as well as in tangent spaces to Riemannian manifolds, ''normalize'' means to scale by a factor to make the norm equal to 1.~~		{{:Normal monomorphism}}

			{{:Normal epimorphism}}

	===In probability/statistics===		===In probability/statistics===

	~~[[Find link::Normal distribution]]: A particular kind of distribution parametrized by mean and variance, also called the Gaussian distribution.~~		{{:Normal distribution}}

	~~[[Find link:~~:Normal ~~random variable]]: A random variable whose distribution is a normal~~ distribution.

	===Others===		===Others===

	~~[[mathworld~~:~~NormalNumber\|~~Normal number~~]] to base <math>b</math>: A real number that, when written in base <math>b</math>, has all digits occurring with equal probability.~~		{{:Normal number}}

	~~[[mathworld:AbsolutelyNormal\|Absolutely normal number]]: A real number that is positive to base <math>b</math> for every integer <math>b > 1</math>.~~

Vipul: /* In differential geometry */

2008-06-09T14:09:42Z

In differential geometry

← Older revision		Revision as of 14:09, 9 June 2008
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	Normal to a curve in the plane: The line perpendicular to the tangent to the curve at a point.		Normal to a curve in the plane: The line perpendicular to the tangent to the curve at a point.

	~~[[Diffgeom~~:Normal bundle\|Normal bundle]] to a submanifold, or immersed manifold: The quotient of the tangent bundle to the whole manifold (restricted to the submanifold), by the tangent bundle to the submanifold, or immersed manifold. When the manifolds are Riemannian, the normal bundle can be viewed as the orthogonal complement to the tangent bundle of the submanifold, in the tangent bundle to the whole manifold.		{{:Normal bundle}}

	~~[[Diffgeom~~:Normal coordinate system~~\|Normal coordinate system]] refers to a particular kind of local coordinate system for a Riemannian manifold.~~		{{:Normal coordinate system}}

	~~Vectors in the normal bundle are termed normal vectors.~~

	===In normed vector spaces===		===In normed vector spaces===

Vipul at 13:59, 9 June 2008

2008-06-09T13:59:04Z

← Older revision		Revision as of 13:59, 9 June 2008
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	===In Galois theory===		===In Galois theory===

	~~[[Find link:~~:Normal field extension~~]]: A field extension is termed normal if the fixed field under the automorphism group of the extension, is precisely the base field.~~		{{:Normal field extension}}

	===In commutative algebra===		===In commutative algebra===

	~~[[Commalg~~:Normal domain~~\|Normal domain]]: An integral domain is termed normal if it is integrally closed in its field of fractions.~~		{{:Normal domain}}

	~~[[Commalg~~:Normal ring~~\|Normal ring]]: A commutative unital ring is termed normal if it is integrally closed in its total quotient ring~~		{{:Normal ring}}

	===In differential geometry===		===In differential geometry===

Vipul at 13:48, 9 June 2008

2008-06-09T13:48:30Z

← Older revision		Revision as of 13:48, 9 June 2008
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	* To denote something upright or perpendicular		* To denote something upright or perpendicular
	* To denote something that is as it ''should be''. In this sense, normal means ''good'' or ''desirable'' rather than ''typical''		* To denote something that is as it ''should be''. In this sense, normal means ''good'' or ''desirable'' rather than ''typical''

			It is typically used as a limiting adjective, and in a binary sense. In other words, an object in a certain class is ''normal'' if it satisfies certain conditions, and every object in that class is either normal or not normal. The noun form is ''normality''. Thus, normality can be viewed as a property in various contexts.

	===In group theory===		===In group theory===
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	===In linear algebra===		===In linear algebra===

	~~[[Find link:~~:Normal form~~]], also called canonical form, is a standard form in which to put a matrix~~ (~~typically, upto conjugation~~)~~. Two normal forms commonly used are the Jordan normal form and the rational normal form.~~		{{:Normal form (linear algebra)}}

			{{:Normal matrix}}

	~~[[Find link:~~:Normal ~~matrix]]: A matrix over the complex numbers, with the property that it commutes with its conjugate-transpose.~~		{{:Normal operator}}
	===In Galois theory===		===In Galois theory===

Vipul at 16:31, 14 May 2008

2008-05-14T16:31:15Z

← Older revision		Revision as of 16:31, 14 May 2008
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	===In group theory===		===In group theory===

	~~[[Groupprops~~:Normal subgroup~~\|Normal subgroup]]: A subgroup of a group that occurs as the kernel of a homomorphism, or equivalently, such that every left coset and right coset are equal.~~		{{:Normal subgroup}}

	Related terms: Normality (the property of a subgroup being normal), [[Groupprops:Normal core\|normal core]] (the largest normal subgroup contained in a given subgroup), [[Groupprops:Normal closure\|normal closure]] (the smallest normal subgroup containing a given subgroup), [[Groupprops:Normalizer\|normalizer]] (the largest subgroup containing a given subgroup, in which it is normal).

	Term variations: [[Groupprops:Subnormal subgroup\|subnormal subgroup]], [[Groupprops:Abnormal subgroup\|abnormal subgroup]], [[Groupprops:Quasinormal subgroup\|quasinormal subgroup]], and others. See [[Groupprops:Category:Variations of normality]], [[Groupprops:Category:Opposites of normality]], and [[Groupprops:Category:Analogues of normality]].

	===In topology===		===In topology===

	~~[[Topospaces~~:Normal space~~\|Normal space]]: A topological space is termed normal if all points are closed sets (the <math>T_1</math> assumption), and any two disjoint closed subsets can be separated by disjoint open subsets.~~		{{:Normal space}}

	~~In some definitions, the <math>T_1</math> assumption is skipped.~~

	~~Related terms: normality (the property of a topological space being normal)~~

	~~Term variations: [[Topospaces:Category:Variations of normality\|Variations of normality]] offers a list.~~

	===In linear algebra===		===In linear algebra===

Vipul at 01:52, 13 May 2008

2008-05-13T01:52:29Z

← Older revision		Revision as of 01:52, 13 May 2008
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	===In differential geometry===		===In differential geometry===

			Normal to a curve in the plane: The line perpendicular to the tangent to the curve at a point.

	[[Diffgeom:Normal bundle\|Normal bundle]] to a submanifold, or immersed manifold: The quotient of the tangent bundle to the whole manifold (restricted to the submanifold), by the tangent bundle to the submanifold, or immersed manifold. When the manifolds are Riemannian, the normal bundle can be viewed as the orthogonal complement to the tangent bundle of the submanifold, in the tangent bundle to the whole manifold.		[[Diffgeom:Normal bundle\|Normal bundle]] to a submanifold, or immersed manifold: The quotient of the tangent bundle to the whole manifold (restricted to the submanifold), by the tangent bundle to the submanifold, or immersed manifold. When the manifolds are Riemannian, the normal bundle can be viewed as the orthogonal complement to the tangent bundle of the submanifold, in the tangent bundle to the whole manifold.
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	[[Find link::Normal random variable]]: A random variable whose distribution is a normal distribution.		[[Find link::Normal random variable]]: A random variable whose distribution is a normal distribution.

			===Others===

			[[mathworld:NormalNumber\|Normal number]] to base <math>b</math>: A real number that, when written in base <math>b</math>, has all digits occurring with equal probability.

			[[mathworld:AbsolutelyNormal\|Absolutely normal number]]: A real number that is positive to base <math>b</math> for every integer <math>b > 1</math>.

Vipul: /* In probability/statistics */

2008-05-13T01:20:52Z

In probability/statistics

← Older revision		Revision as of 01:20, 13 May 2008
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	===In probability/statistics===		===In probability/statistics===

	Normal distribution: A particular kind of distribution parametrized by mean and variance, also called the Gaussian distribution.		[[Find link::Normal distribution]]: A particular kind of distribution parametrized by mean and variance, also called the Gaussian distribution.

	Normal random variable: A random variable whose distribution is a normal distribution.		[[Find link::Normal random variable]]: A random variable whose distribution is a normal distribution.