A characterization of normal matrices by their exponentials (Q913903)

A complex \(n\times n\)-matrix A is normal if and only if the functions, log \(s_ j(e^{tA})\), \(j=1,2,...,n\) are convex on \({\mathbb{R}}\), where \(s_ 1(B)\geq...\geq s_ n(B)\geq 0\) denote the singular values of \(B\in {\mathbb{C}}^{n\times n}\).