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

作　　者：代丽芳[1] 梁茂林[1] 

机构地区：[1]天水师范学院数学与统计学院,甘肃天水741001

出　　处：《天水师范学院学报》2017年第2期10-12,共3页Journal of Tianshui Normal University

基　　金：天水师范学院中青年教师项目"大型稀疏Sylvester型矩阵方程的高效算法及理论"(TAS1603))阶段性成果

摘　　要：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.

关 键 词：正交投影 广义投影对称矩阵 左右逆特征值问题 最佳逼近 

分 类 号：O241.6[理学—计算数学]