矩阵方程AX =B的自反最小秩解及其最佳逼近

摘要

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.