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 problem—both for the student and for the professor. Of course, the concept of a trick is not uniquely defined—by 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.
Author(s): Simo Puntanen, George P. H. Styan, Jarkko Isotalo (auth.)
Edition: 1
Publisher: Springer-Verlag Berlin Heidelberg
Year: 2011
Language: English
Pages: 486
Tags: Statistical Theory and Methods
Front Matter....Pages i-xvii
Introduction....Pages 1-56
Easy Column Space Tricks....Pages 57-70
Easy Projector Tricks....Pages 71-90
Easy Correlation Tricks....Pages 91-104
Generalized Inverses in a Nutshell....Pages 105-120
Rank of the Partitioned Matrix and the Matrix Product....Pages 121-144
Rank Cancellation Rule....Pages 145-150
Sum of Orthogonal Projectors....Pages 151-154
A Decomposition of the Orthogonal Projector....Pages 155-190
Minimizing cov(y - Fx)....Pages 191-214
BLUE....Pages 215-266
General Solution to AYB = C....Pages 267-282
Invariance with Respect to the Choice of Generalized Inverse....Pages 283-290
Block-Diagonalization and the Schur Complement....Pages 291-304
Nonnegative Definiteness of a Partitioned Matrix....Pages 305-316
The Matrix $$\dot{\rm M}$$ ....Pages 317-342
Disjointness of Column Spaces....Pages 343-348
Full Rank Decomposition....Pages 349-356
Eigenvalue Decomposition....Pages 357-390
Singular Value Decomposition....Pages 391-414
The Cauchy–Schwarz Inequality....Pages 415-426
Back Matter....Pages 427-486
