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Generalization of Roth's solvability criteria to systems of matrix equations
Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap.
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
2017. Vol. 527, s. 294-302
Emneord [en]
Systems of matrix equations, Sylvester equations, Roth's criteria
HSV kategori
Identifikatorer
URN: urn:nbn:se:umu:diva-136303DOI: 10.1016/j.laa.2017.04.011ISI: 000402344000014OAI: oai:DiVA.org:umu-136303DiVA, id: diva2:1117626
Forskningsfinansiär
Swedish Research Council, E0485301Tilgjengelig fra: 2017-06-29 Laget: 2017-06-29 Sist oppdatert: 2019-04-18bibliografisk kontrollert

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