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

Author(s)

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

• Document type: Journal article
• Source: Linear Algebra and its Applications; v. 510, p. 246-258, DEC 1 2016.
• Web of Science Citations: 8

Abstract

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)

• 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