Roth’s solvability criteria for the matrix equations AX - XB^ = C and X - AXB^ = C over the skew field of quaternions with aninvolutive automorphism q ¿ qˆ
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hdl:2117/102143
Tipus de documentArticle
Data publicació2016-12-01
EditorElsevier
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Abstract
The matrix equation AX-XB = C has a solution if and only if the matrices A C 0 B and A 0
0 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 0 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 ^ XB = C over the skew field of quaternions with a fixed involutive automorphism q ¿ ˆq.
CitacióFutorny, V., Klymchuk, T., Sergeichuk , V. Roth’s solvability criteria for the matrix equations AX - XB^ = C and X - AXB^ = C over the skew field of quaternions with aninvolutive automorphism q ¿ qˆ. "Linear algebra and its applications", 1 Desembre 2016, vol. 510, p. 246-258.
ISSN0024-3795
Versió de l'editorhttp://www.sciencedirect.com/science/article/pii/S0024379516303597
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