具有正规特征值的矩阵的刻画

Characterization of matrices with some normal eigenvalues

如果一个复方阵的一个特征值所对应的每个右特征向量一定也是左特征向量,则称其为正规特征值.本文给出了具有正规特征值的矩阵的结构.作为应用,给出了谱半径等于谱范数的矩阵结构.

An eigenvalue A of a complex square matrix A is called a normal eigenvalue if every right eigenvector of A associated with A need be a left eigenvector of A associated with A. In this paper, a structural characterization is given for the class of those matrices with some normal eigenvalues. And then use it to determine the structure of matrices satisfying it＇ s the spectral radius is equal to it＇ s the spectral norm.