Differentiability of functions of matrices
classification
🧮 math.FA
math.RT
keywords
functionmatricesextensionalphaanalyticityclassconjugationdiagonal
read the original 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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