Total derivatives of eigenvalues and eigenprojections of symmetric matrices

Karl K. Brustad

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arXiv · 1905.06045

Total derivatives of eigenvalues and eigenprojections of symmetric matrices

Karl K. Brustad

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Abstract

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 $Ω\subseteq\mathbb{R}^n$.

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Karl K. Brustad. 2019-05-15. Total derivatives of eigenvalues and eigenprojections of symmetric matrices. https://arxiv.org/abs/1905.06045

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