The Generalized Bisymmetric (Bi-Skew-Symmetric) Solutions of a Class of Matrix Equations and Its Least Squares Problem

Abstract

The solvability conditions and the general expression of the generalized bisymmetric and bi-skew-symmetric solutions of a class of matrix equations $(AX=B$, $XC=D)$ are established, respectively. If the solvability conditions are not satisfied, the generalized bisymmetric and bi-skew-symmetric least squares solutions of the matrix equations are considered. In addition, two algorithms are provided to compute the generalized bisymmetric and bi-skew-symmetric least squares solutions. Numerical experiments illustrate that the results are reasonable.