Analysis of Symmetric Matrix Valued Functions
H. Mohebi, Abbas Salemi · Numerical Functional Analysis and Optimization · 2007
For any symmetric function f: ℝ n → ℝ 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.