Localization of the Matrix Spectrum and Lyapunov Type Equations

The problems on the location of the matrix spectrum inside or outside domains bounded by ellipses or parabolas are studied. Special Lyapunov-type equations are connected with these problems. Theorems about the unique solvability of such equations are proved. Conditions for perturbations of matrix en...

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Bibliographic Details
Published in:Lobachevskii journal of mathematics 2024, Vol.45 (4), p.1808-1818
Main Authors: Demidenko, G. V., Wang, Z.
Format: Article
Language:English
Subjects:
Algebra
Analysis
Geometry
Mathematical Logic and Foundations
Mathematics
Mathematics and Statistics
Probability Theory and Stochastic Processes
Online Access:Get full text
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Summary:The problems on the location of the matrix spectrum inside or outside domains bounded by ellipses or parabolas are studied. Special Lyapunov-type equations are connected with these problems. Theorems about the unique solvability of such equations are proved. Conditions for perturbations of matrix entries are obtained, which guarantee that the spectra of the perturbed matrices belong to the specified domains as well.
ISSN:1995-0802
1818-9962
DOI:10.1134/S1995080224601358