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arXiv · 1810.01464

Perturbation theory for the matrix square root and matrix modulus

Marcus Carlsson
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Abstract

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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Marcus Carlsson. 2018-10-02. Perturbation theory for the matrix square root and matrix modulus. https://arxiv.org/abs/1810.01464

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