Roth's solvability criteria for the matrix equations AX - (X)over-capB = C and X - A(X)over-capB = C over the skew field of quaternions with an involutive automorphism q -> (q)over-cap

Autor(es)

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

• Tipo de documento: Artigo Científico
• Fonte: Linear Algebra and its Applications; v. 510, p. 246-258, DEC 1 2016.
• Citações Web of Science: 8

Resumo

The matrix equation AX - XB = C has a solution if and only if the matrices {[}A C 0 B] and {[}A 0 o B] are similar. This criterion was proved over a field by W.E. Roth (1952) and over the skew field of quaternions by Huang Liping (1996). H.K. Wimmer (1988) proved that the matrix equation X - AXB = C over a field has a solution if and only if the matrices {[}A C 0 I] and {[}I 0 L B] are simultaneously equivalent to {[}A 0 0 I] and {[}I 0 0 B]. We extend these criteria to the matrix equations AX - XB = C and X - A (X) over capB = C over the skew field of quaternions with a fixed involutive automorphism q -> (q) over cap. (C) 2016 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