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Coupled Sylvester-type Matrix Equations and Block Diagonalization
Department of Computing Science and HPC2N, Umeå University, Umeå, Sweden.ORCID iD: 0000-0001-9110-6182
Department of Computing Science and HPC2N, Umeå University, Umeå, Sweden.
2015 (English)In: SIAM Journal on Matrix Analysis and Applications, ISSN 0895-4798, E-ISSN 1095-7162, Vol. 36, no 2, p. 580-593Article in journal (Refereed) Published
Abstract [en]

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 $2 \times 2$ 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.

Place, publisher, year, edition, pages
Society for Industrial and Applied Mathematics, 2015. Vol. 36, no 2, p. 580-593
Keywords [en]
matrix equation, Sylvester equation, Stein equation, Roth's theorem, consistency, block diagonalization
National Category
Computer Sciences Mathematical Analysis
Identifiers
URN: urn:nbn:se:oru:diva-74892DOI: 10.1137/151005907ISI: 000357407800011Scopus ID: 2-s2.0-84936772205OAI: oai:DiVA.org:oru-74892DiVA, id: diva2:1332892
Available from: 2019-06-28 Created: 2019-06-28 Last updated: 2019-09-20Bibliographically approved

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Dmytryshyn, AndriiKågström, Bo

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  • apa
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  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
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  • text
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