Abstract:

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.

Key words: submatrix constraint, inverse generalized eigenvalue problem, generalized reflexive solutions, optimal approximation, perturbation analysis