矩阵方程AX=B的自反最小秩解及其最佳逼近

The reflexive minimal rank solution of the matrix equation AX = B and the optimal approximation

利用矩阵对的广义奇异值分解,得到了矩阵方程AX=B有自反解的充分必要件,以及有解时,定秩解、最小秩解的一般表达式.另外,给出了自反最小秩解集合中与给定矩阵的最佳逼近解.

By applying the generalized singular value decomposition of matrix pairs, the necessary and sufficient conditions are obtained for the existence of the reflexive solutions of the matrix equation AX = B, and the expression of the fixed and minimal rank solutions is also shown. In addition, for the minimal rank solution set, the expression of the optimal approximation solution to a given matrix is derived.