In this paper,the problem for matrix equation of X,Y was solued,when A and B satisfy the same singular value decomposition(SSVD). The symetric solution and the sufficient and necessary conditions were obtained and the minimum-Frobenius-norm symmetric solution was given.
The inverse problem for matrix equation of X,Y,AX + YB = C(A、B and C are m×n matrixies)was solved ,when A and B satisfied the samesingular value decomposition (SSVD). We sought the symmetric matrix X∈SRn×n ,Y∈SRm×m,to satisfy || AX + YB - C || F = min,and obtained the minimum-Frobenius-norm symmetric solution.
In this paper,the problem for matrix equation of X,Y was solued,when A and B satisfy the same singular value decomposition(SSVD).The symetric solution and the sufficient and necessary conditions were obtained and the minimum-Frobenius-norm symmetric solution was given.
In this paper,the inverse problem for matrix equation of X:‖AXB~T+BXA~T-C‖_F=min,AXB~T+BXA~T=C is considered,when A and B satisfy the same singular value decomposition(SSVD).The symmetric solution is obtained and the minimum-Frobenius-norm symmetric solution is given.
An Optimal Opproximation of matrix-fibres under linear constrains was solved with the modifying of the condition. The inverse problem for matrix equation of X,Y,AX + YB = C(A、B and C are m×n matrixies)was solved ,when A and B satisfied the samesingular value decomposition (SSVD). We sought the symmetric matrix X∈SRn×n ,Y∈SRm×m,to satisfy || AX + YB - C || F = min,and obtained the minimum-Frobenius-norm symmetric solution.