一类特殊矩阵的逆特征值问题

INVERSE EIGENVALUE PROBLEMS FOR A CLASS OF SPECIAL MATRICES

本文研究了一类具有特殊形式的矩阵A的两个逆特征值问题.利用箭形矩阵和Jacobi矩阵的性质,将此类矩阵逆特征值问题转换为线性方程组问题,得到了问题有唯一解的充分必要条件,给出了解的表达式及相应数值例子,推广了箭形矩阵和Jacobi矩阵逆特征值问题.

In this paper, we study two inverse eigenvalue problems of a class of matrix A with special form. By using the properties of arrow matrix and Jacobi matrix, we transform the inverse eigenvalue problem of this kind of matrix into a system of linear equations. The necessary and sufficient conditions for the problem to have a unique solution are obtained, and the expressions of the understanding and the corresponding numerical examples are given, which is a generalization of the inverse eigenvalue problem of the arrow shaped matrix and the Jacobi matrix.