Eigenvalue Interlacing Of Real Symmetric Matrices

Matrix is one of the most basic concepts in algebra,and the real symmetric matrix is of great research significance.The theoretical study of eigenvalue of real symmetric matrix is undoubtedly the most exciting and valuable part.Estimation the eigenvalue range of the matrices can often play a very important role in computational mathematics,image processing,etc.By using Rayleigh’s principle,this paper discusses the staggered relationship between the eigenvalues of two real symmetric matrices in the case of S^TS=diag（d₁,···,d_m）,and then uses the conclusion to discuss the situation of SS^T=diag（d₁,···,d_m,0,···,0）.Finally,the real symmetric matrices will be considered as matrices in blocks,with the help of matrix transformation and disc theorem,the gen-eralized interlacing between the eigenvalues of the matrix from main diagonal line and the partial eigenvalues of the original matrix is obtained.