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

Abstract

W.E. Roth (1952) proved that the matrix equation AX-XB=C has a solution if and only if the matrices View the MathML source and View the MathML source are similar. A. Dmytryshyn and B. Kågström (2015) extended Roth's criterion to systems of matrix equations View the MathML source(i=1,…,s) with unknown matrices X1,…,Xt, in which every Xs is X , X¿, 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.