English

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.

Keywords

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}
}
R2 v1 2026-06-23T04:26:27.600Z