An extended collection of matrix derivative results for forward and reverse mode automatic differentiation

Abstract

This paper collects together a number of matrix derivative results which are very useful in forward and reverse mode algorithmic differentiation (AD). It highlights in particular the remarkable contribution of a 1948 paper by Dwyer and Macphail which derives the linear and adjoint sensitivities of a matrix product, inverse and determinant, and a number of related results motivated by applications in multivariate analysis in statistics.

This is an extended version of a paper which will appear in the proceedings of AD2008, the 5th International Conference on Automatic Differentiation.