ON LOG-SUBHARMONICITY OF SINGULAR-VALUES OF MATRICES

Let F be an analytic function from an open subset Omega of the complex plane into the algebra of n x n matrices. Denoting by s(1),...,s(n) t he decreasing sequence of singular values of a matrix, we prove that t he functions log s(1)(F(lambda)) +...+ log s(k)(F(lambda)) and log(+) s(1)(F(lambda)) +...+ log(+) s(k)(F(lambda) are subharmonic on Omega f or 1 less than or equal to k less than or equal to n.