Least-Squares Solutions of Matrix Equations(AX = B,XC = D) for Hermitian Reflexive (Anti-Hermitian Reflexive) Matrices and Its Approximation

摘要

In this paper,the Hermitian reflexive(Anti-Hermitian reflexive)least-squares so-lutions of matrix equations(AX = B,XC = D)are considered.With special properties of partitioned matrices and Hermitian reflexive(Anti-Hermitian reflexive)matrices,the general expression of the solution is obtained.Moreover,the related optimal approximation problem to a given matrix over the solution set is considered.