Mo logo [home] [lexicon] [problems] [tests] [courses] [auxiliaries] [notes] [staff] german flag
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 overview
The matrix powers $ A^n$, $ n=0,1,\ldots$, converge to the zero matrix if and only if the absolute value of each eigenvalue $ \lambda$ is smaller than $ 1$.

The sequence $ (A^n)$ is bounded if $ \vert\lambda\vert\le 1$ and algebraic and geometric multiplicity are equal for eigenvalues of modulus $ 1$.

If there exists an eigenvalue of modulus greater than $ 1$, then the sequence diverges.

(Authors: Burkhardt/Höllig/Hörner)

see also:

[Annotations]
  automatically generated 2/10/2005