An extension of Yamamoto's theorem on the eigenvalues and singular values of a matrix
Huajun Huang, Tin-Yau Tam · Journal of the Mathematical Society of Japan · 2006
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 ) | .