New Bounds Of The Spread Of Matrices

The study on eigenvalues of matrices is one of the most basic and important content in matrix theory. The matrix spread is a description of distribution of eigenvalues for a matrix, and has important significance in matrix theory and its applications. In this thesis, several bounds of a matrix spread are given. Firstly, two new upper bounds of a matrix spread, which improved the corresponding results in recent literatures, are obtained based on previous research on of the spread matrix, and the theoretical results are illustrated with examples. Secondly, the lower bounds of the matrix spread are studied, and a new lower bound is obtained.