An extension of Yamamoto's theorem on the eigenvalues and singular values of a matrix
TAM, Tin-Yau ; HUANG, Huajun
J. Math. Soc. Japan, Tome 58 (2006) no. 3, p. 1197-1202 / Harvested from Project Euclid
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We extend, in the context of real semisimple Lie group, a result of T. Yamamoto which asserts that $\lim_{m\to \infty} [s_i(X^m)]^{1/m} = |\lambda_i(X)|$ , $i=1, \dots , n$ , where $s_1(X)\ge \cdots \ge s_n(X)$ are the singular values, and $\lambda_1(X), \dots , \lambda_n(X)$ are the eigenvalues of the $n\times n$ matrix $X$ , in which $|\lambda_1(X)|\ge \cdots \ge |\lambda_n(X)|$ .
Publié le : 2006-10-14
Classification:  Yamamoto's theorem,  Cartan decomposition,  complete multiplicative Jordan decomposition,  15A45,  22E46 
@article{1179759544,
     author = {TAM, Tin-Yau and HUANG, Huajun},
     title = {An extension of Yamamoto's theorem on the eigenvalues and singular values of a matrix},
     journal = {J. Math. Soc. Japan},
     volume = {58},
     number = {3},
     year = {2006},
     pages = { 1197-1202},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1179759544}
}

TAM, Tin-Yau; HUANG, Huajun. An extension of Yamamoto's theorem on the eigenvalues and singular values of a matrix. J. Math. Soc. Japan, Tome 58 (2006) no. 3, pp.  1197-1202. http://gdmltest.u-ga.fr/item/1179759544/