Difference between revisions of "Eigenvalue"
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| − | In [[linear algebra]], an '''eigenvector''' of a [[linear map]] <math>L</math> | + | In [[linear algebra]], an '''eigenvector''' of a [[linear map]] <math>L</math> is a non-zero [[vector]] <math>\bold{v}</math> such that applying <math>L</math> to <math>\bold{v}</math> results in a vector in the same direction as <math>v</math> (including possibly the zero vector). In other words, <math>\bold{v}</math> is an eigenvector for <math>L</math> if and only if there is some scalar constant <math>\lambda</math> such that <math>L \bold{v} = \lambda \bold{v}</math>. Here, <math>\lambda</math> is known as the '''eigenvalue''' associated to the eigenvector. The '''eigenspace''' of an eigenvalue refers to the set of all eigenvectors that correspond with that eigenvalue, and is a [[vector space]]; in particular, it is a subspace of the domain of the map <math>L</math>. |
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[[Category:Linear algebra]] | [[Category:Linear algebra]] | ||
Latest revision as of 18:32, 2 March 2010
In linear algebra, an eigenvector of a linear map 
is a non-zero vector 
such that applying to results in a vector in the same direction as 
(including possibly the zero vector). In other words, is an eigenvector for if and only if there is some scalar constant 
such that 
. Here, is known as the eigenvalue associated to the eigenvector. The eigenspace of an eigenvalue refers to the set of all eigenvectors that correspond with that eigenvalue, and is a vector space; in particular, it is a subspace of the domain of the map .
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