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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 (engelsk)Inngår i: Linear Algebra and its Applications, ISSN 0024-3795, E-ISSN 1873-1856, Vol. 527, s. 294-302Artikkel i tidsskrift (Fagfellevurdert) 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.

sted, utgiver, år, opplag, sider
Elsevier, 2017. Vol. 527, s. 294-302
Emneord [en]
Systems of matrix equations, Sylvester equations, Roth's criteria
HSV kategori
Identifikatorer
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
Forskningsfinansiär
Swedish Research Council, E0485301eSSENCE - An eScience Collaboration
Merknad

Research funders:

National Council for Scientific and Technological Development CNPq

São Paulo Research Foundation FAPESP

Tilgjengelig fra: 2019-06-28 Laget: 2019-06-28 Sist oppdatert: 2019-09-20bibliografisk kontrollert

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