一类次对称矩阵的左右逆特征值问题

Left and Right Inverse Eigenvalue Problems of a Class of Skew-symmetric Matrices

研究了下列问题:已知A,C∈Rn×m,B,D∈Rl×n,找X∈M SRn×n,使X A=C BX=成立,其中M SRn×n表示n阶次对称矩阵的集合。讨论了该问题有解的充要条件,并在有解时,给出了通解的一般表达式。

In this paper, the following problems are investigated： Given A A,C∈R^n×m,B,D∈R^l×n,find X∈MSR^n×n,make that{XA=C BX=D ,where MSR^n×n is set of all skew-symmetric matrices of n rank. The necessary and sufficient conditions for the solutions of the problem are discussed. The expressions for the solutions of the problem are also given.