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

Author(s)

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

• Document type: Journal article
• Source: Linear Algebra and its Applications; v. 527, p. 294-302, AUG 15 2017.
• Web of Science Citations: 6

Abstract

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)

• FAPESP's process: 14/09310-5 - Algebraic structures and their representations
• Grantee: Vyacheslav Futorny
• Support Opportunities: Research Projects - Thematic Grants
• FAPESP's process: 15/05864-9 - Classification problems in linear algebra and system theory
• Grantee: Vyacheslav Futorny
• Support Opportunities: Research Grants - Visiting Researcher Grant - International