Study On The Eigenvalues And Singular Value Of Matrices And The Spectral Radius Of Non-Negative Matrices

Matrix calculations and matrix analysis have wide application in economics, computational mathematics, computer graphics and image analysis. This paper studies the smallest singular value of matrices, the spectral radius of non-negative matrix and the existence of matrix eigenvalues. The thesis consists of five chapters.The first chapter mainly provides the development of matrix and the numerical characteristics of matrix. Then we introduce a special matrix—nonnegative matrix, we tell significance of the Perron root.The second chapter gives an overview of the smallest singular value and gives one good results of the smallest singular value by some nature of M matrix and Blocks matrix, this At last, we give an example about this.The third chapter gives some spectral radius of one special matrix—non-negative matrix. In this chapter we mainly gives some the below sequences by the theory of the iteration matrix and blocks matrix.The forth chapter gives an overview of matrix eigenvalues and introduces some scholars study about the existing regional of matrix eigenvalues the characteristic value exist in the domain (by the multiple plates to a disc), and the scholars gives some good results in recent years.The last chapter gives summary of all the content and illustrates the research content of this paper.