Derivative operations on matrices

1 April 1970

journal article
Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Automatic Control

Vol. 15 (2) , 241-244
https://doi.org/10.1109/tac.1970.1099409

Abstract

The structure of a matrix derivative on a matrix valued function is defined. Matrix product and chain rules are developed which provide significant simplifications for obtaining derivatives of compound matrix structures, and some closed-form structures for Taylor's expansions of a matrix in terms of derivatives and elements of a second matrix are given.

Keywords

AUTOMATIC CONTROL
CONTROL SYSTEMS
DELAY SYSTEMS
OPTIMAL CONTROL
COUNCILS
LINEAR SYSTEMS
NONLINEAR CONTROL SYSTEMS
HISTORY
MATRICES
EQUATIONS

This publication has 2 references indexed in Scilit:

A direct derivation of the optimal linear filter using the maximum principle
IEEE Transactions on Automatic Control, 1967
The matrix minimum principle
Information and Control, 1967