摘要
利用矩阵的奇异值分解及广义逆,给出了矩阵约束下矩阵反问题AX=B有实对称解的充分必要条件及其通解的表达式.此外,给出了在矩阵方程的解集合中与给定矩阵的最佳逼近解的表达式.
By using the singular va lu e decomposition(SVD) and Morre-Penrose inverse of matrices,this paper establishe s the necessary and sufficient conditions for the existence of and the expressio ns for the symmetric solutions of matrix inverse problem AX=B under a submat rix constraint.In addition,in the solution set of corresponding equation,the express ion of the optimal approximation solution to a given matrix in Frobenius norm is derived.
出处
《数学理论与应用》
2005年第2期117-120,共4页
Mathematical Theory and Applications
