Matrix equations under semi-Tensor ProductAx=B; XC=DLeast Squares solution

Abstract

 In this paper, we study the matrix equations under the semi-tensor product.Ax=B; XC=DThe least squares solution under Different ConditionsX^{The following}2.R^P£q,Where MatrixA 2R^{M £ n}B 2R^{H £ K}C 2R^{A £ B}D 2R^{L £ d}Given.According to the definition of semi-tensor product, it is transformed into matrix equations under ordinary product.,Combined with the Matrix Singular Value Decomposition and matrix differential, the analytic expression of the least squares solution of the equations under different circumstances is given.,And it is verified by numerical examples..