On log-subharmonicity of singular values of matrices
Volume 122 / 1997
Studia Mathematica 122 (1997), 195-200
DOI: 10.4064/sm-122-2-195-200
Abstract
Let F be an analytic function from an open subset Ω of the complex plane into the algebra of n×n matrices. Denoting by $s_1,...,s_n$ the decreasing sequence of singular values of a matrix, we prove that the functions $log s_{1}(F(λ)) + ... + log s_{k}(F(λ))$ and $log^{+}s_{1}(F(λ)) + ... + log^{+}s_{k}(F(λ))$ are subharmonic on Ω for 1 ≤ k ≤ n.
