一类广义对称矩阵的左右逆特征值问题及其最佳逼近

The Left and Right Inverse Eigen problem for a Class of Generalized Symmetric Matrices and the Associated Approximation Problem

基于正交投影变换,给出了广义投影对称矩阵的定义,并讨论了其结构特性.在此基础上,考虑了此类广义对称矩阵的左右逆特征值问题的可解性条件,并得到其通解表达式.同时,对任意给定矩阵得到了相应最佳逼近问题的唯一解.

The generalized projective symmetric matrices are put forward by means of the orthogonal projection transformations,and some properties of which are presented.The solvability conditions of the left and right inverse eigenproblem for the above generalized symmetric matrices are obtained,and the general solution is derived.Meanwhile,for any given matrix,the unique solution to the associated optimal approximate problem is given.