We extend, in the context of real semisimple Lie group, a result of T. Yamamoto which asserts that , , where are the singular values, and are the eigenvalues of the matrix , in which .
"An extension of Yamamoto's theorem on the eigenvalues and singular values of a matrix." J. Math. Soc. Japan 58 (4) 1197 - 1202, October, 2006. https://doi.org/10.2969/jmsj/1179759544