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Generalization of Roth's solvability criteria to systems of matrix equations
Department of Computing Science, Umeå University, Umeå, Sweden.ORCID iD: 0000-0001-9110-6182
Department of Mathematics, University of São Paulo, São Paulo, Brazil.
Universitat Politècnica de Catalunya, Barcelona, Spain; Taras Shevchenko National University, Kiev, Ukraine.
Institute of Mathematics, Kiev, Ukraine.
2017 (English)In: Linear Algebra and its Applications, ISSN 0024-3795, E-ISSN 1873-1856, Vol. 527, p. 294-302Article 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
Elsevier, 2017. Vol. 527, p. 294-302
Keywords [en]
Systems of matrix equations, Sylvester equations, Roth's criteria
National Category
Mathematical Analysis
Identifiers
URN: urn:nbn:se:oru:diva-74884DOI: 10.1016/j.laa.2017.04.011ISI: 000402344000014Scopus ID: 2-s2.0-85017553149OAI: oai:DiVA.org:oru-74884DiVA, id: diva2:1332905
Funder
Swedish Research Council, E0485301eSSENCE - An eScience Collaboration
Note

Research funders:

National Council for Scientific and Technological Development CNPq

São Paulo Research Foundation FAPESP

Available from: 2019-06-28 Created: 2019-06-28 Last updated: 2019-09-20Bibliographically approved

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Dmytryshyn, Andrii

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Citation style
  • apa
  • harvard1
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  • vancouver
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More styles
Language
  • de-DE
  • en-GB
  • en-US
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  • nn-NO
  • nn-NB
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  • Other locale
More languages
Output format
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