A formula for the 2-norm distance from a matrix to the set of matrices with multiple eigenvalues

被引：0

作者：

Malyshev, AN ^{[1
]}

机构：

[1] Univ Bergen, Dept Informat, N-5020 Bergen, Norway

来源：

NUMERISCHE MATHEMATIK | 1999年 / 83卷 / 03期

关键词：

Mathematics Subject Classification (1991):65F15, 65F35;

D O I：

10.1007/s002110050458

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove that the 2-norm distance from an n x n matrix A to the matrices that have a multiple eigenvalue lambda is equal to [GRAPHICS] where the singular values ar, are ordered nonincreasingly. Therefore, the 2-norm distance from A to the set of matrices with multiple eigenvalues is [GRAPHICS] Mathematics Subject Classification (1991): 65F15, 65F35.

引用

页码：443 / 454

页数：12

共 50 条

[21] Sufficient conditions for error distance reduction in the t2 2-norm trust region between minimizers of local nonconvex multivariate quadratic approximates
Xie, Pengcheng
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2025, 453
[22] The distance from a matrix polynomial to matrix polynomials with a prescribed multiple eigenvalue
Papathanasiou, Nikolaos
Psarrakos, Panayiotis
LINEAR ALGEBRA AND ITS APPLICATIONS, 2008, 429 (07) : 1453 - 1477
[23] A Corrector for the Sample Mahalanobis Distance Free from Estimating the Population Eigenvalues of Covariance Matrix
Kobayashi, Yasuyuki
NEURAL INFORMATION PROCESSING, ICONIP 2016, PT II, 2016, 9948 : 224 - 232
[24] THE D1/2-NORM OF THE SOR AND CYCLIC CHEBYSHEV SEMI-ITERATIVE (CCSI) METHODS FOR A CLASS OF NON-SYMMETRIC MATRICES
EVANS, DJ
LI, C
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, 1989, 27 (03) : 547 - 557
[25] Matrix differential calculus applied to multiple stationary time series and an extended Whittle formula for information matrices
Klein, Andre
Spreij, Peter
LINEAR ALGEBRA AND ITS APPLICATIONS, 2009, 430 (2-3) : 674 - 691
[26] Denoising and completion of Euclidean distance matrix from multiple observations
Natva, Sai Sumanth
Nannuru, Santosh
2024 NATIONAL CONFERENCE ON COMMUNICATIONS, NCC, 2024,
[27] ON THE DISTANCE FROM A WEAKLY NORMAL MATRIX POLYNOMIAL TO MATRIX POLYNOMIALS WITH A PRESCRIBED MULTIPLE EIGENVALUE
Kokabifar, E.
Loghmani, G. B.
Psarrakos, P. J.
ELECTRONIC JOURNAL OF LINEAR ALGEBRA, 2016, 31 : 71 - 86
[28] MULTIPLE RECURRENCES AND THE ASSOCIATED MATRIX STRUCTURES STEMMING FROM NORMAL MATRICES
Mertens, Clara
Vandebril, Raf
SIAM JOURNAL ON NUMERICAL ANALYSIS, 2014, 52 (06) : 2977 - 2999
[29] Localization From Structured Distance Matrices via Low-Rank Matrix Recovery
Lichtenberg, Samuel
Tasissa, Abiy
IEEE TRANSACTIONS ON INFORMATION THEORY, 2024, 70 (12) : 8929 - 8941
[30] Bounding the diameter and the mean distance of a graph from its eigenvalues:: Laplacian versus adjacency matrix methods
Rodríguez, JA
Yebra, JLA
DISCRETE MATHEMATICS, 1999, 196 (1-3) : 267 - 275

← 1 2 3 4 5 →