The Diagonal Elements Have The Separation Of Nonzero Matrices Of K Zero Elements

The eigenvalues of matrices have important applications in physics, management science and engineering, economics, biology, image analysis etc. The spread of a matrix is one of the hot issues which the eigenvalues of matrices research.Based on the recent works of Roman Dronvsek about the spread of a nonnegative matrix [Roman Drnovsek, The spread of the spectrum of a nonnegative matrix with a zero diagonal element, Linear Algebra Appl.439(2013)2381-1387], we do further research on this issue. First, we improve the results of Roman Dronvsek and obtain a new lower bound of the spread of a nonnegative matrix with a zero diagonal element. Then, we research the spread of a nonnegative matrix with k zero diagonal entries and obtain several lower bounds of the spread. Finally, we discuss the spread of a nonnegative matrix with k zero diagonal entries which eigenvalues are all real, and a lower bound of the spread is obtained.