Analysis of Symmetric Matrix Valued Functions |
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Authors: | H. Mohebi A. Salemi |
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Affiliation: | 1. Mahani Mathematical Research Center, University of Kerman , Kerman, Iran hmohebi@mail.uk.ac.ir;3. Mahani Mathematical Research Center, University of Kerman , Kerman, Iran |
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Abstract: | For any symmetric function f: ? n → ? n , one can define a corresponding function on the space of n × n real symmetric matrices by applying f to the eigenvalues of the spectral decomposition. We show that this matrix valued function inherits from f the properties of continuity, Lipschitz continuity, strict continuity, directional differentiability, Fréchet differentiability, and continuous differentiability. |
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Keywords: | Continuous differentiability Directional differentiability Fréchet differentiability Lipschitz continuity Spectral function Strict continuity Symmetric matrix valued function |
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