An extension of Yamamoto's theorem on the eigenvalues and singular values of a matrix
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 \(\left| \lambda _{1}(X)\right| \geq \dots \geq \left| \lambda _{n}(X)\right| \).
complete multiplicative Jordan decomposition
scientific article; zbMATH DE number 5119788
scientific article