【摘 要】
：
Let T1,n be an n × n unreduced symmetric tridiagonal matrix with eigenvalues λ1 ＜ λ2 ＜ … ＜ λn. and is an (n - 1) × (n - 1) submatrix by deleting the kth row
【机 构】
：
Department of Mathematics, Shanghai University, Shanghai 200436, China
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Let T1,n be an n × n unreduced symmetric tridiagonal matrix with eigenvalues λ1 ＜ λ2 ＜ … ＜ λn. and is an (n - 1) × (n - 1) submatrix by deleting the kth row and kth column, k = 1, 2,…, n from Tn. Let μ1 ≤μ2 ≤ … ≤μk-1 be the eigenvalues of T1,k-1 and μk ≤μk+1 ≤ … ≤μn-1 be the eigenvalues of Tk+1,n.A new inverse eigenvalues problem has put forward as follows: How do we construct an unreduced symmetric tridiagonal matrix T1,n, if we only know the spectral data: the eigenvalues of T1,n, the eigenvalues of T1,k_1 and the eigenvalues of Tk+1,n ? Namely if we only know the data: λ1, λ2,…, λn, μ1,μ2, …,μk-1 and μk,μk+1,…,μn-1 how do we find the matrix T1,n? A necessary and sufficient condition and an algorithm of solving such problem, are given in this paper.
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