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arXiv · math/0310086

Differentiability of functions of matrices

Yury Grabovsky·Omar Hijab·Igor Rivin
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Abstract

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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Yury Grabovsky, Omar Hijab, Igor Rivin. 2003-10-07. Differentiability of functions of matrices. https://arxiv.org/abs/math/0310086

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