实广义自反矩阵左右逆特征值问题

Left and right inverse eigenvalue problem of real general reflexive matrices

给出了实广义自反矩阵的定义及相关性质,利用矩阵的奇异值分解,讨论了实广义自反矩阵左右逆特征值及其最佳逼近问题,得到了其通解表达式,并给出了此问题的最佳逼近解以及求最佳逼近解的数值算法和算例.

The definition and some characters of general reflexive matrix are given, By applying the singular-value decomposition（SVD） the general solutions of the Problem of left and right inverse eigenvalue for general reflexive matrix are obtained, and the optimal approximate solution is found. And the numeral algorithm and the example of optimal approximation solution are given.