• 论文 •

Hermite矩阵特征值反问题的几乎处处不可解性

1. 中国科学院计算中心
• 出版日期:1987-03-14 发布日期:1987-03-14

THE UNSOLVABILITY OF INVERSE EIGENVALUE PROBLEMS FOR HERMITIAN MATRIX ALMOST EVERYWHERE

1. Ye Qiang Computing Center. Academia Sinica
• Online:1987-03-14 Published:1987-03-14
§1.引言 Hermite矩阵的特征值反问题是Downing和Householder在[2]中提出的,其形式如下: 问题A. 给定Hermite矩阵A,k个非零实数λ_1…,λ_k,以及满足r_+r_1+…+r_k=n的k+1个非负整数r_1,r_1,…,r_k,求一实对角矩阵D=diag(d_1,…,d_n),使得A+D的特征值为0,λ_1,…,λ_k,并且相应的重数为 r_0,r_1,…,r_k.
In this paper, the unsolvability of inverse eigenvalue problems for the hermitian matrixalmost everywhere is discussed. The method used in [6] and [7] is applied here, and somesimilar results are obtained.
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 [1] L. Auslander, Differential Geometry, Harper & Row, 1967． [2] A. C. Downing, A. S. Householder, Some inverse characteristic value problems, J. Assoc. Comp. Math.3(1956) , 203-207． [3] K. P. Hadeler, Ein inverses eigenwertproblem, Linear Algebra Appl.,1(1968) , 83--101． [4] K. P. Hadeler, Multiplikative inverses eigenwertproblem, Lincar Algebra Appl. 2(1969) , 65--86． [5] A. Shapiro, On the unsolvability of inverse eigenvalue problems almost everywhere, Linear Algebra Appl.49(1983) , 27--31． [6] Sun Ji-guang The unsolvability of multiplicative inverse eigenvalue problems almost everywhere, J. Comp.Math. 4: 3 (1986) . 227--244． [7] Sun Ji-guang, Ye Qiang, The unsolvability of inverse algebraic eigenvalue problems almost everywhere. J.Comp. Math. 4: 3 (1986) , 212--226． [8] S. Sternberg, Lectures on Differential Geometry, Prentice-Hall, Englewood Cliffs, N. J. 1964．
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