Matrix Eigenvalue And Singular Value Estimate

This paper investigates the estimations for matrix eigenvalues and singular values. For matrices of high orders, it is very difficult to obtain their exact eigenvalues or singular values, so it is particularly important to local the eigenvalues or singular values by rows, columns or minors of matrices. The main works and results of this paper are as follows:First, new eigenvalue inclusion sets for partitioned matrices in the complex plane are obtained by uniting the result of partitioned matrices and Cvetkocic, L, Kostic, V., and Varga.Second, based on an improvement on Fy Fan's theorem of matrix eigenvalues[1-2], two types of new estimates for matrix singular values are presented.