Differentiability of functions of matrices
Grabovsky, Yury · Hijab, Omar · Rivin, Igor
Original · EN
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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