由谱数据构造实双反对称矩阵(英文)

CONSTRUCTION OF REAL BI-ANTISYMMETRIC MATRICES WITH PRESCRIBED SPECTRUM DATA

讨论实完全反对称矩阵的一个特征值反问题.研究了实完全反对称矩阵的一些特征性质,构造一个实反对称矩阵使其各阶顺序主子矩阵具有指定的特征值.证明了:给定满足一定分隔条件的两组数,存在一个实完全反对称矩阵,使其各阶中心主子矩阵具有相应的特征值.

In this paper,we present an inverse eigenvalue problem for real bi-antisymmetric matrices. We investgate some eigen-properties of the real bi-antisymmetric matrices. Then we describe how to construct a real anti-symmetric matrix which has the specified spectral data in its leading submatrices. As the conclution of this paper we prve that： for given two sets of numbers which satisfy certain interlace conditions, there exists a real antisymmetric matrix whose central submatrices have prescribed spectrum data.