Journal of the Mathematical Society of Japan

An extension of Yamamoto's theorem on the eigenvalues and singular values of a matrix

Huajun HUANG and Tin-Yau TAM

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Abstract

We extend, in the context of real semisimple Lie group, a result of T. Yamamoto which asserts that lim m [ s i ( X m ) ] 1 / m = | λ i ( X ) | , i = 1 , , n , where s 1 ( X ) s n ( X ) are the singular values, and λ 1 ( X ) , , λ n ( X ) are the eigenvalues of the n × n matrix X , in which | λ 1 ( X ) | | λ n ( X ) | .

Article information

Source
J. Math. Soc. Japan, Volume 58, Number 4 (2006), 1197-1202.

Dates
First available in Project Euclid: 21 May 2007

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1179759544

Digital Object Identifier
doi:10.2969/jmsj/1179759544

Mathematical Reviews number (MathSciNet)
MR2276188

Zentralblatt MATH identifier
1117.15008

Subjects
Primary: 15A45: Miscellaneous inequalities involving matrices 22E46: Semisimple Lie groups and their representations

Keywords
Yamamoto's theorem Cartan decomposition complete multiplicative Jordan decomposition

Citation

TAM, Tin-Yau; HUANG, Huajun. An extension of Yamamoto's theorem on the eigenvalues and singular values of a matrix. J. Math. Soc. Japan 58 (2006), no. 4, 1197--1202. doi:10.2969/jmsj/1179759544. https://projecteuclid.org/euclid.jmsj/1179759544


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References

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