Anti-diagonals of symmetric and skew symmetric matrices with prescribed eigenvalues

被引：1

作者：

Yan, Wen

Tam, Tin-Yau ^{[1
]}

机构：

[1] Auburn Univ, Dept Math & Stat, Auburn, AL 36849 USA

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2013年 / 438卷 / 03期

关键词：

kth Anti-diagonal; Eigenvalues; Weak majorization; SINGULAR VALUES; ELEMENTS; THEOREMS;

D O I：

10.1016/j.laa.2012.08.038

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The complete relationship between the kth anti-diagonals and the eigenvalues of an n x n (k <= n) real symmetric matrix is obtained. When k is even, the relationship is weak majorization. The Hermitian case is also studied. Similar results are obtained for real and complex skew symmetric matrices. (C) 2012 Elsevier Inc. All rights reserved.

引用

页码：1446 / 1453

页数：8

共 50 条

[41] On computing of arbitrary positive integer powers for one type of odd order skew-symmetric tridiagonal matrices with eigenvalues on imaginary axis-II
Rimas, Jonas
[J]. APPLIED MATHEMATICS AND COMPUTATION, 2007, 186 (01) : 872 - 878
[42] On computing of arbitrary positive integer powers for one type of even order skew-symmetric tridiagonal matrices with eigenvalues on imaginary axis-II
Rimas, Jonas
[J]. APPLIED MATHEMATICS AND COMPUTATION, 2006, 181 (02) : 1120 - 1125
[43] Eigenvalues of matrices with several prescribed blocks, II
Cravo, G
Silva, FC
[J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 2003, 364 : 81 - 89
[44] Generalized derivatives of eigenvalues of a symmetric matrix
Stechlinski, Peter
[J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 2022, 649 (63-95) : 63 - 95
[45] Matrix inverse problem and its optimal approximation problem for R-skew symmetric matrices
Huang, Guang-Xin
Yin, Feng
Chen, Hua-Fu
Chen, Ling
Guo, Ke
[J]. APPLIED MATHEMATICS AND COMPUTATION, 2010, 216 (12) : 3515 - 3521
[46] A parallel algorithm for computing eigenvalues of very large real symmetric matrices on message passing architectures
Balle, S
Cullum, J
[J]. APPLIED NUMERICAL MATHEMATICS, 1999, 30 (2-3) : 341 - 365
[47] A fast recursive algorithm for constructing matrices with prescribed eigenvalues and singular values
Chu, MT
[J]. SIAM JOURNAL ON NUMERICAL ANALYSIS, 2000, 37 (03) : 1004 - 1020
[48] A. HORN'S RESULT ON MATRICES WITH PRESCRIBED SINGULAR VALUES AND EIGENVALUES
Tam, Tin-Yau
[J]. ELECTRONIC JOURNAL OF LINEAR ALGEBRA, 2010, 21 : 25 - 27
[49] A smoothing spline algorithm to interpolate and predict the eigenvalues of matrices extracted from the sequence of preconditioned banded symmetric Toeplitz matrices
Kouser, Salima
Rehman, Shafiq Ur
Alsaiari, Mabkhoot
Ahmad, Fayyaz
Jalalah, Mohammed
Harraz, Farid A.
Akram, Muhammad
[J]. AIMS MATHEMATICS, 2024, 9 (06): : 15782 - 15795
[50] A SKEW-SYMMETRIC LANCZOS BIDIAGONALIZATION METHOD FOR COMPUTING SEVERAL EXTREMAL EIGENPAIRS OF A LARGE SKEW-SYMMETRIC MATRIX
Huang, Jinzhi
Jia, Zhongxiao
[J]. SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 2024, 45 (02) : 1114 - 1147

← 1 2 3 4 5 →