Generalization of Roth's solvability criteria to systems of matrix equations

Autor(es)

Dmytryshyn, Andrii ; Futorny, Vyacheslav ; Klymchuk, Tetiana ; Sergeichuk, Vladimir V.

• Tipo de documento: Artigo Científico
• Fonte: Linear Algebra and its Applications; v. 527, p. 294-302, AUG 15 2017.
• Citações Web of Science: 6

Resumo

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. (AU)

• Processo FAPESP: 14/09310-5 - Estruturas algébricas e suas representações
• Beneficiário: Vyacheslav Futorny
• Modalidade de apoio: Auxílio à Pesquisa - Temático
• Processo FAPESP: 15/05864-9 - Problemas de classificação em álgebra linear e teoria de sistemas
• Beneficiário: Vyacheslav Futorny
• Modalidade de apoio: Auxílio à Pesquisa - Pesquisador Visitante - Internacional