对称矩阵与反对称矩阵广义特征值反问题的拓广

A Generalization of the Inverse GeneralizedEigenvalue Problem for Symmetric and Anti-Symmetric Matrices

定义了上三角等次对角线矩阵和上三角交错次对角线矩阵;讨论了矩阵方程AX-XA=0的对称解与AX+XA=0的反对称解.在此基础上考虑了以下问题的可解性:给定A∈Rn×m,D∈Rm×m,分别求X,Y∈SRn×n和X,Y∈ASRn×n,使得XA=YDA.

This paper defined up-triangle equal minor diagonal matrix and up-triangle stagger minor diagonal matrix. The Symmetric solution of matrix equation AX-XA=0 and anti-symmetric solution of matrix equation AX＋XA=0 are discussed. Further, the following problem is considered： given A ∈ R^n×m, D∈ R^m×m, find X,Y∈SR^n×m and X,Y∈ASR^m×m , such that X=AYAD respectively.