Собствени стойност и собствени вектори на матрица - Revision history

Anko at 16:55, 17 December 2012

2012-12-17T16:55:48Z

Anko at 16:54, 17 December 2012

2012-12-17T16:54:21Z

Anko at 16:45, 17 December 2012

2012-12-17T16:45:20Z

Anko: Created page with "In this [[shear mapping the red arrow changes direction but the blue arrow does not. The blue arrow is an eigenvector, and sin..."

2012-12-17T16:38:14Z

Created page with "thumb|270px|In this [[shear mapping the red arrow changes direction but the blue arrow does not. The blue arrow is an eigenvector, and sin..."

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	[[File:Mona Lisa eigenvector grid.png\|thumb\|270px\|In this [[shear mapping]] the red arrow changes direction but the blue arrow does not. The blue arrow is an eigenvector, and since its length is unchanged its eigenvalue is 1.]]		[[File:Mona Lisa eigenvector grid.png\|thumb\|270px\|In this [[shear mapping]] the red arrow changes direction but the blue arrow does not. The blue arrow is an eigenvector, and since its length is unchanged its eigenvalue is 1.]]

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 [[File:Mona Lisa eigenvector grid.png|thumb|270px|In this [[shear mapping]] the red arrow changes direction but the blue arrow does not. The blue arrow is an eigenvector, and since its length is unchanged its eigenvalue is 1.]]
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 [[Category:Articles including recorded pronunciations]]
 [[Category:German loanwords]]

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 For example, if three-element vectors are seen as arrows in three-dimensional space, an eigenvector of a 3×3 matrix ''A'' is an arrow whose direction is either preserved or exactly reversed after multiplication by ''A''. The corresponding eigenvalue determines how the length and sense of the arrow is changed by the operation.
-Specifically, a non-zero column vector ''v'' is a '''right eigenvector''' of a matrix ''A'' if (and only if) there exists a number ''λ'' such that ''Av'' = ''λv''. If the vector satisfies ''vA'' = ''λv'' instead, it is said to be a '''left eigenvector'''. The number ''λ'' is called the '''eigenvalue''' corresponding to that vector. The set of all eigenvectors of a matrix, each paired with its corresponding eigenvalue, is called the '''eigensystem''' of that matrix.<ref name=WolframEigenvector>{{Cite web
+Specifically, a non-zero column vector ''v'' is a '''right eigenvector''' of a matrix ''A'' if (and only if) there exists a number ''λ'' such that ''Av'' = ''λv''. If the vector satisfies ''vA'' = ''λv'' instead, it is said to be a '''left eigenvector'''. The number ''λ'' is called the '''eigenvalue''' corresponding to that vector. The set of all eigenvectors of a matrix, each paired with its corresponding eigenvalue, is called the '''eigensystem''' of that matrix.
-| title=Eigenvector
 An '''eigenspace''' of ''A'' is the set of all eigenvectors with the same eigenvalue, together with the [[zero vector]].<ref name=WolframEigenvector/>