左右逆特征值问题及其最佳逼近问题的(R,S)对称矩阵解

On(R,S)-symmetric matrix solutions of left and right inverse eigenvalue problem and its corresponding best approximation problem

令R∈Cm×m和S∈Cn×n是2个非平凡卷积矩阵,即R=R-1≠±Im,且S=S-1≠±In。如果一个矩阵A∈Cm×n满足RAS=A,则矩阵A称为(R,S)对称矩阵。本文首先分别给出了左右逆特征值问题的(R,S)对称矩阵解的可解条件和一般表达式;然后,给出了左右逆特征值问题相应的最佳逼近问题的(R,S)对称矩阵解。

Let R∈Cm×m and S∈Cn×n be two nontrivial involutions,i.e.,R=R-1≠±Im and S=S-1≠±In.A matrix A∈Cm×n is called（R,S）-symmetric matrix if A is satisfactory to RAS=A.This paper first gives the solvable conditions and the general expressions of the（R,S）-symmetric solutions for the left and right inverse eigenvalue problem.Then,the corresponding best approximation problem to the left and right inverse eigenvalue problem is also solved over（R,S）-symmetric matrix solution.