Analysis of symmetric matrix valued functions I

For any symmetric function f : R-n -> R-n, one can define a corresponding function on the space of n x n real symmetric matrices by applying f to the eigenvalues of the spectral decomposition. We show that this matrix valued function inherits from f the properties of continuity, Lipschitz continuity, strict continuity, directional differentiability, Frechet differentiability, continuous differentiability. (C) 2007 Elsevier Ltd. All rights reserved.