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Linear matrix equations: The module theoretic approach. (English) Zbl 0677.15001

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.
Reviewer: G.P.Barker

MSC:

15A24 Matrix equations and identities
12D10 Polynomials in real and complex fields: location of zeros (algebraic theorems)
16D80 Other classes of modules and ideals in associative algebras
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