摘要
该文考察以下2个逆特征值问题：（I）问题（SA）：设A＝（aij）为n阶实对称矩阵，其主对角元aii＝0，i＝1，2，…，n。给定对角矩阵A＝diag（λ1，λ2，…，λn）∈Rn×n求一实对角矩阵X＝diag（x1，x2，…，xn）∈Rn×n，使λ（A＋X）＝λ（Λ）。（Ⅱ）问题（SM）：设A＝（aij）为n阶实对称矩阵，其主对角元aii＝1，i＝1，2，…，n。给定对角矩阵Λ＝dias（λ1，λ2，…，λn）∈Rn×n，求一实对角矩阵X＝diag（x1，x2，…，xn），使λ（XA）一人（A）。对上述这2问题得到用特征值分离度表示的可解的必要条件，利用连续映射的映射度概念，给出上述问题可解的充分条件。这些条件改进了已知结果。
The following two inverse eigenvalue problems are considered in this paper.(I ) Problem (SA): let A= (AIJ) be an n×n real symmetric matrix whose main diagonal entries as= O, i= l, 2, …,n. For a given real diagonal matrix A=diag (γ1,γ2,...,γn), find a real diagonal matrix X = diag (x1,,x2, …,xn), such that γ (i= 1, 2, …, n) are eigenvalues of the sum A+X. (I ) Problem (SM): let A= (as) be an n X n real symmetric matrix whose main diagonal entries op = 1,i= 1, …,n. For a given real diagonal matrix A=diag (γ1,γ2, ...γn), find a real diagonal matrix X = diag (x1,,x2, ..., xn ) such that γi (i = 1, 2, ..., n) are eigenvalues of the product XA. For the two above problems, a necessary cond1tlon is obtained for the solubility of problem (SA) and problem (SM), which are expressions using eigenvalue spread, respectively. Using the mapping degree conception of continuous mapping, a sufficient condition is given for the two above problems. These conditions can improve the known results relative to inverse eigenvalue problem.
出处
《南京理工大学学报》
EI
CAS
CSCD
1997年第3期281-284,共4页
Journal of Nanjing University of Science and Technology
基金
南京理工大学校科研基金
