主子阵约束下广义自反矩阵的广义特征值反问题

利用矩阵的奇异值分解和商奇异值分解, 建立子矩阵约束下广义特征值反问题的广义自反解存在的充分必要条件, 并给出通解的表达式. 对任意给定矩阵的最佳逼近问题, 得到了最佳逼近广义自反解, 并对最佳逼近解进行扰动分析.

Inverse Generalized Eigenvalue Problem for GeneralizedReflexive Matrices under a Submatrix Constraint

Using the singular value decomposition (SVD) and quotient singular value decomposition (QSVD) of a matrix and matrix pair, the authors established the necessary and sufficient conditions for the existence of the generalized reflexive solutions and the expressions for the inverse generalized eigenvalue problem of a matrix under a submatrix constraint. Moreover, the optimal approximation problem to a given matrix in the solution set was considered, and the optimal approximation generalized reflexive solution was obtained, and the perturbation analysis was made.