Differentiability of functions of matrices

Yury Grabovsky, Omar Hijab, Igor Rivin

Published 2003-10-07Version 1

Given a function on diagonal matrices, there is a unique way to extend this to an invariant (by conjugation) function on symmetric matrices. We show that the extension preserves regularity -- that is, if the original function is k times differentiable so is the extension (likewise for analyticity and the class k+alpha).