In this paper,sufficient and necessary condition of existence of orthogonal solution for the matrix equation AXB=D is deduced by applying spectral and singular value decom-positions of matrices,and the expression of orthogonal solution to this matrix equation is also provided.Furthermore,the associated optimal approximate problem to the given matrix is discussed and the expression of optimal approximate orthogonal solution is derived.Finally,one numerical experiment is given to validate the correctness of the theories.
spectral decompositionsingular value decompositionmatrix equationorthog-onal solutionoptimal approximation
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