Perturbation theory for the matrix square root and matrix modulus
Marcus Carlsson · arXiv (Cornell University) · 2018
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 Fréchet differentiability formulas provided by the Daleckii-Krein theorem.