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Generalization of Roth's solvability criteria to systems of matrix equations
Umeå University, Faculty of Science and Technology, Department of Computing Science.
2017 (English)In: Linear Algebra and its Applications, ISSN 0024-3795, E-ISSN 1873-1856, Vol. 527, 294-302 p.Article in journal (Refereed) Published
Abstract [en]

W.E. Roth (1952) proved that the matrix equation AX - XB = C has a solution if and only if the matrices [Graphics] and [Graphics] are similar. A. Dmytryshyn and B. Kagstrom (2015) extended Roth's criterion to systems of matrix equations A(i)X(i')M(i) - (NiXi"Bi)-B-sigma i = Ci (i = 1,..., s) with unknown matrices X1,, X-t, in which every X-sigma is X, X-T, or X*. We extend their criterion to systems of complex matrix equations that include the complex conjugation of unknown matrices. We also prove an analogous criterion for systems of quaternion matrix equations. (C) 2017 Elsevier Inc. All rights reserved.

Place, publisher, year, edition, pages
2017. Vol. 527, 294-302 p.
Keyword [en]
Systems of matrix equations, Sylvester equations, Roth's criteria
National Category
Mathematical Analysis
Identifiers
URN: urn:nbn:se:umu:diva-136303DOI: 10.1016/j.laa.2017.04.011ISI: 000402344000014OAI: oai:DiVA.org:umu-136303DiVA: diva2:1117626
Funder
Swedish Research Council, E0485301
Available from: 2017-06-29 Created: 2017-06-29 Last updated: 2017-06-29Bibliographically approved

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