Matrix Differential Calculus with Applications in Statistics and Econometrics

by Jan R. Magnus, Heinz Neudecker

This book provides a unified treatment of matrix differential calculus, specifically written for econometricians and statisticians. Divided into six parts, the book begins with a treatment of matrix algebra, discussing the Schur, Jordan, and singular-value decompositions, the Hadamard and Kronecker products, and more. The second section is the theoretical core of the book and presents a thorough development of the theory of differentials. Practically-oriented, part three contains the rules for working with differentials and lists the differentials of important scalar, vector, and matrix functions. The fourth deals with inequalities, such as Cauchy-Schwarz's and Minkowski's, while the fifth section is devoted to applications of matrix differential calculus to the linear regression model. The book closes by detailing maximum likelihood estimation, an ideal source for demonstrating the power of the propagated techniques. Features numerous exercises.

Genres: Mathematics

416 pages, Hardcover

First published April 25, 1988

Reviews

[Lucille Nguyen · Rating 4 out of 5]

Two points:

1) this is a fairly good coverage of differential calculus with matrices and its applications to maximum likelihood estimation statistics

2) probably the worst notation for the transpose I've ever seen in a math book. Using ' to denote the transpose makes sense if you're MATLAB-brained, but c'mon, \intercal T superscript is both more readable and understandable at a glance

Good for a overview + review of the topic. Probably wouldn't use it as a first book on the subject tbh