Perturbation theory for the matrix square root and matrix modulus

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 Fréchet differentiability formulas provided by the Daleckii-Krein theorem.

References in corpus (1)

• Perturbation theory for the spectral decomposition of Hermitian matrices

Cited by in corpus (4)

• Stochastic Canonical Correlation Analysis
• Perturbation Theory for Quantum Information
• Perturbation theory for the spectral decomposition of Hermitian matrices
• For Manifold Learning, Deep Neural Networks can be Locality Sensitive Hash Functions