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On the equality of algebraic and geometric multiplicities of matrix eigenvalues

โœ Scribed by J. Ding; Noah H. Rhee

Publisher
Elsevier Science
Year
2011
Tongue
English
Weight
213 KB
Volume
24
Category
Article
ISSN
0893-9659

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โœฆ Synopsis

We summarize seventeen equivalent conditions for the equality of algebraic and geometric multiplicities of an eigenvalue for a complex square matrix. As applications, we give new proofs of some important results related to mean ergodic and positive matrices.

๐Ÿ“œ SIMILAR VOLUMES

On the sensitivity of multiple eigenvalu
On the sensitivity of multiple eigenvalues of nonsymmetric matrix pencils
โœ Huiqing Xie; Hua Dai ๐Ÿ“‚ Article ๐Ÿ“… 2003 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 158 KB

This paper considers the sensitivity of semisimple multiple eigenvalues and corresponding generalized eigenvector matrices of a nonsymmetric matrix pencil analytically dependent on several parameters. The directional derivatives of the multiple eigenvalues are obtained, and the average of eigenvalue