EPr Solution to a System of Matrix Equations

摘要

A square complex matrix is called if it can be written in the form with being fixed unitary and being arbitrary matrix in . We give necessary and sufficient conditions for the existence of the solution to the system of complex matrix equation and present an expression of the solution to the system when the solvability conditions are satisfied. In addition, the solution to an optimal approximation problem is obtained. Furthermore, the least square solution with least norm to this system mentioned above is considered. The representation of such solution is also derived.