Mathematics-Online lexicon: Powers of Matrices

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	Mathematics-Online lexicon:
	Powers of Matrices

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

be a matrix having an eigenvalue $\lambda$ of largest absolute value with associated eigenvector

. If vector

has a nontrivial component in the eigenspace of $\lambda$ , that is, if

with $c\ne0$ and $u\nparallel v$ , then we have

$\displaystyle A^n x = \lambda^n (c u + o(1)),\quad n\to\infty \,.$

(Authors: App/Burkhardt/Höllig)

Examples:

automatically generated 2/10/2005