New Inclusion Sets For Eigenvalues Of Matrices With Invariant Main Diagonal Elements

Eigenvalue estimation of matrices is a very hot topic in matrix theory.As a class of special matrices,matrices with invariant main diagonal elements have important applications in image processing,differential and integral equations theory,etc.Firstly,in this thesis,a new inclusion set for eigenvalues of matrices with invariant main diagonal elements is obtained by using an existing sufficient condition for the nonsingularity of matrices with invariant main diagonal elements.Secondly,two new sufficient conditions of nonsingularity of matrices with invariant main diagonal elements are given by using the nonsingularity of double α1-matrices and double α2-matrices and two new inclusion sets for eigenvalues of matrices with invariant main diagonal elements are obtained.Finally,the obtained results are applied to Toeplitz matrices and three new inclusion sets for eigenvalues of Toeplitz matrices are obtained.Numerical examples are given to show that the results improve several existing results in some cases.