Matrix Tricks for Linear Statistical Models Our Personal Top Twenty [Hardcover]

In teaching linear statistical models to first-year graduate students or to final-year undergraduate students there is no way to proceed smoothly without matrices and related concepts of linear algebra; their use is really essential. Our experience is that making some particular matrix tricks very familiar to students can substantially increase their insight into linear statistical models (and also multivariate statistical analysis). In matrix algebra, there are handy, sometimes even very simple tricks which simplify and clarify the treatment of a problemboth for the student and for the professor. Of course, the concept of a trick is not uniquely definedby a trick we simply mean here a useful important handy result.
In this book we collect together our Top Twenty favourite matrix tricks for linear statistical models.Introduction.- Easy Column Space Tricks.- Easy Projector Tricks.- Easy Correlation Tricks.- Generalized Inverses in a Nutshell.- Rank of the Partitioned Matrix and the Matrix Product.- Rank Cancellation Rule.- Sum of Orthogonal Projector.- Minimizing cov(y - Fx).- BLUE.- General Solution to AYB = C.- Invariance with Respect to the Choice of Generalized Inverse.- Block-Diagonalization and the Schur Complement.- Nonnegative Definiteness of a Partitioned Matrix.- The Matrix M.- Disjointness of Column Spaces.- Full Rank Decomposition.- Eigenvalue Decomposition.- Singular Value Decomposition.- The Cauchy-Schwarz Inequality.- Notation.- References.- Author Index.- Subject Index.

From the reviews:

It is for everyone who works on the properties of (multivariate) linear statistical models, especially for graduate students in statistics. Also, the book is & for experts who have had an introduction to multivariate models and have a big preference for matrix results. & book is full of recent results and advances of linear algebra related linear statistical models over the last decades. & book has the potentl#œ