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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
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