Applications of Matrix Derivatives To Optimization Problem in Statistical Pattern Recognition

摘要

A necessary condition for a real valued Frechet differentiable function of a vector variable to have an extremum at a vector xo is that the Frechet derivative vanishes at xo. This paper establishes a relationship between Frechet differentials and matrix derivatives obtaining a necessary condition on the matrix derivative at an extrema. These results are applied to various scalar functions of matrix variables which occur in statistical pattern recognition.