Eigenvalues and eigenvectors of Brualdi-Li tournament matrices

Abstract

In this paper, we obtain the result that the characteristic polynomial and the right(left) eigenvectors of Brualdi-Li tournament matrices by new methods, and that the Brualdi-Li tournament matrix has exactly one positive eigenvalue and exactly one negative eigenvalue and the others are complex numbers. In addition, we give that some properties for the eigenvalues and the right(left) eigenvector of Brualdi-Li tournament matrices.