Hermite矩阵特征值反问题的几乎处处不可解性

doi:10.12286/jssx.1987.3.225

计算数学 ›› 1987, Vol. 9 ›› Issue (3): 225-232.DOI: 10.12286/jssx.1987.3.225

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Hermite矩阵特征值反问题的几乎处处不可解性

叶强

中国科学院计算中心

出版日期:1987-03-14 发布日期:1987-03-14

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叶强. Hermite矩阵特征值反问题的几乎处处不可解性[J]. 计算数学, 1987, 9(3): 225-232.

THE UNSOLVABILITY OF INVERSE EIGENVALUE PROBLEMS FOR HERMITIAN MATRIX ALMOST EVERYWHERE

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.

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[8] S. Sternberg, Lectures on Differential Geometry, Prentice-Hall, Englewood Cliffs, N. J. 1964．

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摘要

Hermite矩阵特征值反问题的几乎处处不可解性

THE UNSOLVABILITY OF INVERSE EIGENVALUE PROBLEMS FOR HERMITIAN MATRIX ALMOST EVERYWHERE

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