分块对角型矩阵的广义特征值反问题

已知矩阵X及对角阵以，讨论分块对角型矩阵广义特征值反问题朋=BXA的解A，B]。给出其解的一般表达式及与给定矩阵的最佳逼近解的表达式。进而，证明了广义特征值反问题的对称正交对称解和对称正交反对称解恒存在，给出了其解的一般表达式。

Inverse Generalized Eigenvalue Problem for A Class of Block Diagonal Matrices

Given matrix and diagonal matrix, the block diagonal solutions and its optimal approximation to a given matrix of inverse generalized eigenvalue problem have been considered. The general form of such solutions is given, and the expression of the optimal approximation solution is derived. Further, we show that for such inverse generalized eigenvalue problems, there always exist a symmetric orthogonal symmetric solution and a symmetric orthogonal anti-symmetric solution,and the general forms of such solutions are given.