Journal
SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS
Volume 36, Issue 2, Pages 580-593Publisher
SIAM PUBLICATIONS
DOI: 10.1137/151005907
Keywords
matrix equation; Sylvester equation; Stein equation; Roth's theorem; consistency; block diagonalization
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Funding
- Swedish Research Council (VR) [E0485301]
- eSSENCE, a strategic collaborative e-Science programme - Swedish Research Council
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We prove Roth-type theorems for systems of matrix equations including an arbitrary mix of Sylvester and star-Sylvester equations, in which the transpose or conjugate transpose of the unknown matrices also appear. In full generality, we derive consistency conditions by proving that such a system has a solution if and only if the associated set of 2 x 2 block matrix representations of the equations are block diagonalizable by (linked) equivalence transformations. Various applications leading to several particular cases have already been investigated in the literature, some recently and some long ago. Solvability of these cases follow immediately from our general consistency theory. We also show how to apply our main result to systems of Stein-type matrix equations.
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