Perturbation theory for the matrix square root and matrix modulus
Functional Analysis
2018-10-04 v1
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.
Cite
@article{arxiv.1810.01464,
title = {Perturbation theory for the matrix square root and matrix modulus},
author = {Marcus Carlsson},
journal= {arXiv preprint arXiv:1810.01464},
year = {2018}
}