不可约对称三对角矩阵根的隔离定理的推广  

AN EXTENSION OF THE INTERLACE THEOREM

作　　者：蒋尔雄[1] 

机构地区：[1]上海大学数学系,上海200072

出　　处：《高等学校计算数学学报》1999年第4期305-310,共6页Numerical Mathematics A Journal of Chinese Universities

基　　金：国家自然科学基金资助项目!19771020.

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.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.

关 键 词：三对角矩阵 不可约 对称 根 隔离定理 

分 类 号：O151.21[理学—数学] O241.6[理学—基础数学]