Linear matrix equations: The module theoretic approach (Q1123234)
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scientific article; zbMATH DE number 4108916
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Linear matrix equations: The module theoretic approach |
scientific article; zbMATH DE number 4108916 |
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Linear matrix equations: The module theoretic approach (English)
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1989
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The author discusses solutions to the matrix equation \(\sum \sum f_{ij}A^ iXB^ j=C\) where the matrices have entries from an algebraically closed field K. To do this the author defines a module structure on the set of \(p\times q\) matrices over K derived from the characteristic polynomials of A and B. He utilizes his results to give new proofs for recent results concerning specific equations of interest such as Lyapunov's equation, and to discuss some root location results for polynomials.
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linear matrix equations
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module structure
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characteristic polynomials
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Lyapunov's equation
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root location results for polynomials
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