双中心矩阵特征值反问题的最小二乘解

Least Squares Solutions for the Inverse Problem of Double Center Matrix Eigenvalue

对于矩阵A∈□^(m×n),如果它的每一行元素之和等于零,且每一列元素之和也等于零,则称矩阵A为双中心矩阵.本文利用矩阵的列拉直算子、Moore-Penrose广义逆和一种矩阵向量积讨论n阶双中心矩阵特征值反问题的最小二乘解,得到了矩阵方程AX=X∧的双中心极小范数最小二乘解的表达形式.

For A∈R^m×n , if the sum of the elements in each row and the sum of the elements in ea column are both equal to 0, then A is called a double center matrix. In this paper, we discuss the least squares solutions for the inverse eigenvalue problem of double center matrices with size n by using the vee-operator, the Moore-Penrose generalized inverse and a product of matrices and vectors. We also provide the expression of the least square double center solution with the least norm of the matrix equation AX = XA.