Mathematics-Online lexicon: Generalized Eigenvector, Generalized Eigenspace

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	Mathematics-Online lexicon:
	Generalized Eigenvector, Generalized Eigenspace

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

Let $\lambda$ be an eigenvalue of matrix

with algebraic multiplicity

. A vector

with

$\displaystyle (A-\lambda E)^mv=0\,,\quad v\neq 0$

is called generalised eigenvector for eigenvalue $\lambda$ . All generalised eigenvectors together with the zero vector form a subspace of dimension

called generalised eigenspace $H_\lambda$ for eigenvalue $\lambda$ . This subspace is invariant under the linear mapping

automatically generated 5/17/2011