The *Congruence Class of the Solutions to a System of Matrix Equations

Abstract

We present the $\hspace{0.17em}*$congruence class of the least-square and the minimum norm least-square solutions to the system of complex matrix equation $\mathrm{A}\mathrm{X}=\mathrm{C},\mathrm{ }\mathrm{X}\mathrm{B}=\mathrm{D}$ by generalized singular value decomposition and canonical correlation decomposition.