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Conditions for existence and formulas for the first- and second order totalderivatives of the eigenvalues, and the first order total derivatives of theeigenprojections of smooth matrix-valued functions $H\colon\Omega\to S(m)$ aregiven. The eigenvalues and eigenprojections are considered as functions in thesame domain $\Omega\subseteq\mathbb{R}^n$.

Total derivatives of eigenvalues and eigenprojections of symmetric matrices