不可约对称三对角矩阵根的隔离定理的推广

摘要

Let Tn be an n×n unreduced symmetric tridiagonal matrix with eigenval- ues λ1<λ2<…<λn.Wk is an (n-1)×(n-1) submatrix by deleting the kth row and kth column from Tn,k=1,2,…,n.Letμ1≤μ2≤…≤μn-1, be the eigenvalues of Wk. It is proved that: If Wk has no multiple eigenvalue,then otherwise if μi=μi+1 is any multiple eigenviaue of Wk,then there is instead of above relation μi<λi+1,and retains the residual.