Total derivatives of eigenvalues and eigenprojections of symmetric matrices
Karl K. Brustad · arXiv (Cornell University) · 2019
Conditions for existence and formulas for the first- and second order total derivatives of the eigenvalues, and the first order total derivatives of the eigenprojections of smooth matrix-valued functions $H\colonΩ\to S(m)$ are given. The eigenvalues and eigenprojections are considered as functions in the same domain $Ω\subseteq\mathbb{R}^n$.