# Matrix Algebra From a Statistician's Perspective

Springer Science & Business Media, Jun 27, 2008 - Mathematics - 634 pages
2 Reviews
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Matrix algebra plays a very important role in statistics and in many other dis- plines. In many areas of statistics, it has become routine to use matrix algebra in thepresentationandthederivationorveri?cationofresults. Onesuchareaislinear statistical models; another is multivariate analysis. In these areas, a knowledge of matrix algebra isneeded in applying important concepts, as well as instudying the underlying theory, and is even needed to use various software packages (if they are to be used with con?dence and competence). On many occasions, I have taught graduate-level courses in linear statistical models. Typically, the prerequisites for such courses include an introductory (- dergraduate) course in matrix (or linear) algebra. Also typically, the preparation provided by this prerequisite course is not fully adequate. There are several r- sons for this. The level of abstraction or generality in the matrix (or linear) algebra course may have been so high that it did not lead to a “working knowledge” of the subject, or, at the other extreme, the course may have emphasized computations at the expense of fundamental concepts. Further, the content of introductory courses on matrix (or linear) algebra varies widely from institution to institution and from instructor to instructor. Topics such as quadratic forms, partitioned matrices, and generalized inverses that play an important role in the study of linear statistical models may be covered inadequately if at all.

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### Contents

 Matrices 1 Submatrices and Partitioned Matrices 13 Linear Dependence and Independence 23 Trace of a Square Matrix 49 Consistency and Compatibility 71 Inverse Matrices 79 Generalized Inverses 107 106 Idempotent Matrices 133
 Linear Bilinear and Quadratic Forms 209 Matrix Differentiation 289 Kronecker Products and the Vec and Vech Operators 337 336 Intersections and Sums of Subspaces 379 Sums and Differences of Matrices 419 Minimization of a SecondDegree Polynomial in n Variables 459 The MoorePenrose Inverse 497 496 Eigenvalues and Eigenvectors 521

 Solutions 139 Projections and Projection Matrices 161 Determinants 179
 Linear Transformations 589 References 621 Copyright

### References to this book

 Applied Multivariate AnalysisNeil H. TimmLimited preview - 2007
 The Optimal Design of Blocked and Split-Plot ExperimentsPeter GoosNo preview available - 2002
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