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Generalization of Roth's solvability criteria to systems of matrix equations | | Andrii Dmytryshyn
; Vyacheslav Futorny
; Tetiana Klymchuk
; Vladimir V. Sergeichuk
; | | Date: |
15 Apr 2017 | | Abstract: | W.E. Roth (1952) proved that the matrix equation $AX-XB=C$ has a solution if
and only if the matrices $left[egin{matrix}A&C\0&Bend{matrix}
ight]$ and
$left[egin{matrix}A&0\0&Bend{matrix}
ight]$ are similar. A. Dmytryshyn
and B. K{aa}gstr"om (2015) extended Roth’s criterion to systems of matrix
equations $A_iX_{i’}M_i-N_iX_{i’’}^{sigma_i} B_i=C_i$ $(i=1,dots,s)$ with
unknown matrices $X_1,dots,X_t$, 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. | | Source: | arXiv, 1704.4670 | | Services: | Forum | Review | PDF | Favorites | |
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