一类(0,1)矩阵的谱

Spectra of one kind of(0,1)-matrices

矩阵的特征值是矩阵理论的一个重要概念,然而,求一个矩阵(哪怕是阶数很低的矩阵)的特征值的精确值,却是非常困难的。文章运用图论的理论和方法,巧妙地解决了一类(0,1)矩阵的谱,为(0,1)矩阵的谱理论研究,提供了一种新的思维方法。

The eigenvalues of matrices are an important conception in matrix theory, but computing the precise eigenvalues of a matrix is very difficult. In this paper, the graph theory and method are applied to solve cleverly the spectra of one kind of （0,1）-matrices. This study provides a new mode of thinking for studying the spectra theory of （0,1）-matrices.