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Journal of Convex Analysis 30 (2023), No. 4, 1307--1317
Copyright Heldermann Verlag 2023

On the Differentiability of Symmetric Matrix Valued Functions

Alexander Shapiro
School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, U.S.A.

With every real valued function, of a real argument, can be associated a matrix function mapping a linear space of symmetric matrices into itself. In this paper we study directional differentiability properties of such matrix functions associated with directionally differentiable real valued functions. In particular, we show that matrix valued functions inherit semismooth properties of the corresponding real valued functions.

Keywords: Matrix function, eigenvalues and eigenvectors, directional derivatives, semismooth mappings.

MSC: 15A18, 15A16, 90C30.

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