Perturbation theory for the matrix square root and matrix modulus
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matrixcaseformulasmodulusperturbationrootsquarechet
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We provide first order perturbation formulas for the matrix square root (in the positive semi-definite case) and the matrix modulus (in the general case). The results are new for singular matrices, and extend previously known Fr\'{e}chet differentiability formulas provided by the Daleckii-Krein theorem.
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