See More. Also in Economics. View All. Woke, Inc. Dubner, Stephen J. Armstrong, Martin A. Das Kapital Marx, Karl Paperback. Duflo, Esther Paperback. Discrimination and Disparities Sowell, Thomas Hardcover. Capitalism and Freedom Friedman, Milton Paperback. Buy It Now. Add to cart. Sold by awesomebooksusa About this product Product Information This book presents the reader with new operators and matrices that arise in the area of matrix calculus.
The properties of these mathematical concepts are investigated and linked with zero-one matrices such as the commutation matrix. Elimination and duplication matrices are revisited and partitioned into submatrices. Studying the properties of these submatrices facilitates achieving new results for the original matrices themselves.
Different concepts of matrix derivatives are presented and transformation principles linking these concepts are obtained.
One of these concepts is used to derive new matrix calculus results, some involving the new operators and others the derivatives of the operators themselves. The last chapter contains applications of matrix calculus, including optimization, differentiation of log-likelihood functions, iterative interpretations of maximum likelihood estimators, and a Lagrangian multiplier test for endogeneity.
There is no doubt that the new operators and matrices presented in the book will see their applications in many areas of econometrics. It represents a substantial contribution to our understanding of a difficult area. It is a beautiful book, and destined to become a classic. Mathematical prerequisites; 2. Zero-one matrices; 3. Elimination and duplication matrices; 4. Publication Year:. Item Height:. Cambridge University Press. Item Width:. Economics, Computer Science.
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