Generalization of Roth's solvability criteria to systems of matrix equations
In: eSSENCE – An eScience Collaboration Linear Algebra and its Applications, Jg. 527 (2017), S. 294-302
Online
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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.
| Titel: |
Generalization of Roth's solvability criteria to systems of matrix equations
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| Autor/in / Beteiligte Person: | Dmytryshyn, Andrii ; Futorny, Vyacheslav ; Klymchuk, Tetiana ; Sergeichuk, Vladimir V. |
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| Zeitschrift: | eSSENCE – An eScience Collaboration Linear Algebra and its Applications, Jg. 527 (2017), S. 294-302 |
| Veröffentlichung: | 2017 |
| Medientyp: | unknown |
| ISSN: | 0024-3795 (print) |
| DOI: | 10.1016/j.laa.2017.04.011 |
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