Matrix Derivatives with an Application to an Adaptive Linear Decision Problem

Abstract

A theory of matrix differentiation is presented which uses the concept of a matrix of derivative operators. This theory allows matrix techniques to be used in both the derivation and the description of results. Several new operations and identities are presented which facilitate the process of matrix differentiation. The derivative theorems and new operations are then applied to the problem of determining optimal policies in a linear decision model with unknown coefficients, a problem which would be cumbersome if not impossible to solve without these theorems and operations.