Classes of stable complex matrices defined via the theorems of Geršgorin and Lyapunov

Bryan Cain; Terry D. Lenker; Sivaram K. Narayan; Peter Vermeire

doi:10.1080/03081080701571182

Classes of stable complex matrices defined via the theorems of Geršgorin and Lyapunov

Bryan Cain, Terry D. Lenker, Sivaram K. Narayan, Peter Vermeire

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

We consider (and characterize) mainly classes of (positively) stable complex matrices defined via methods of Gersgorin and Lyapunov. Although the real matrices in most of these classes have already been studied, we sometimes improve upon (and even correct) what has been previously published. Many of the classes turn out quite naturally to be the products of common sets of matrices. A Venn diagram shows how the classes are related.

Original language	English
Pages (from-to)	713-724
Number of pages	12
Journal	Linear and Multilinear Algebra
Volume	56
Issue number	6
DOIs	https://doi.org/10.1080/03081080701571182
State	Published - Nov 2008

Keywords

D-Stability
Diagonal dominance
Gersgorin's theorem
H-matrices
Lyapunov diagonally stable
Lyapunov's theorem
Matrix stability
Positive definite
Strongly sign symmetric

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10.1080/03081080701571182

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abstract = "We consider (and characterize) mainly classes of (positively) stable complex matrices defined via methods of Gersgorin and Lyapunov. Although the real matrices in most of these classes have already been studied, we sometimes improve upon (and even correct) what has been previously published. Many of the classes turn out quite naturally to be the products of common sets of matrices. A Venn diagram shows how the classes are related.",

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AU - Vermeire, Peter

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KW - D-Stability

KW - Diagonal dominance

KW - Gersgorin's theorem

KW - H-matrices

KW - Lyapunov diagonally stable

KW - Lyapunov's theorem

KW - Matrix stability

KW - Positive definite

KW - Strongly sign symmetric

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JF - Linear and Multilinear Algebra

IS - 6

ER -

Classes of stable complex matrices defined via the theorems of Geršgorin and Lyapunov

Abstract

Keywords

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