EPr Solution to a System of Matrix Equations

Changzhou Dong, Yuping Zhang, Jianmin Song

School of Mathematics and Science, Shijiazhuang University of Economics, Shijiazhuang, China.

DOI: 10.4236/alamt.2013.34010                

Abstract

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.

Keywords

EP Matrix; Matrix Equation; Moore-Penrose Inverse; Approximation Problem; Least Squares Solution

Conflicts of Interest

The authors declare no conflicts of interest.

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