An extension of Yamamoto's theorem on the eigenvalues and singular values of a matrix
type: Item
instance of: scholarly article
title: An extension of Yamamoto's theorem on the eigenvalues and singular values of a matrix
zbMATH Open document ID: 1117.15008
author: Huajun Huang
author: Tin-Yau Tam
published in: Journal of the Mathematical Society of Japan
publication date: 2007-01-30T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.jmsj/1179759544
review text: The authors extend, in the context of real semisimple Lie group, a result of T. Yamamoto which asserts that \(\lim_{m\rightarrow \infty }[s_{i}(X^{m})]^{1/m}=\left| \lambda _{i}(X)\right| \), \(i=1,\dots, n,\) where \(s_{1}(X)\geq \dots \geq s_{n}(X)\) are the singular values of the \(n\times n\) matrix \(X\), and \(\lambda _{1}(X),\dots,\lambda _{n}(X)\) are the eigenvalues of \(X\), in which \(\left| \lambda _{1}(X)\right| \geq \dots \geq \left| \lambda _{n}(X)\right| \).
reviewed by: Omar Hirzallah
Mathematics Subject Classification ID: 15A18
Mathematics Subject Classification ID: 15A45
Mathematics Subject Classification ID: 22E46
zbMATH DE Number: 5119788
zbMATH Keywords: Cartan decomposition
zbMATH Keywords: complete multiplicative Jordan decomposition
zbMATH Keywords: semisimple Lie group
MaRDI profile type: Publication
OpenAlex ID: W2053652636
cites work: Q3897665
cites work: Yamamoto's theorem for generalized singular values
cites work: On convexity, the Weyl group and the Iwasawa decomposition
cites work: Two Theorems on Singular Values and Eigenvalues
cites work: Approximation numbers and Yamamoto's theorem in Banach algebras
cites work: Matrices
cites work: On the extreme values of the roots of matrices
DOI: 10.2969/JMSJ/1179759544
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description: scientific article; zbMATH DE number 5119788