Differentiability of functions of matrices

Details Differentiability of functions of matrices Differentiability of functions of matrices

2003-10-07

arxiv.org/abs/math/0310086v1

Mathematics

Functional Analysis

12 pages

Scientific paper

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).

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