A knowledge of matrix algebra is a prerequisite for the study of much of modern statistics, especially the areas of linear statistical models and multivariate statistics. This reference book provides the background in matrix algebra necessary to do research and understand the results in these areas. Essentially self-contained, the book is best-suited for a reader who has had some previous exposure to matrices. Solultions to the exercises are available in the author's "Matrix Algebra: Exercises and Solutions."
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From a review: THE AUSTRALIAN AND NEW ZEALAND JOURNAL OF STATISTICS "This is a book that will be welcomed by many statisticians at most stages of professional development. ...It is essentially a carefully sequenced and tightly interlocking collections of proofs in an elementary, though very pure mathematical style."
From the Publisher
A knowledge of matrix algebra is a prerequisite for the study of much of modern statistics, especially the areas of linear statistical models and multivariate statistics. This reference book provides the background in matrix algebra necessary to do research and understand the results in these areas.
* This book presents matrix algebra in a way that is well-suited for those with an interest in statistics or related disciplines * Includes a number of useful results that have previously only been available from relatively obscure sources * Detailed proofs are provided for all results * The style and level of presentation are designed to make the contents accessible to a broad audience
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Most Helpful Customer Reviews
18 of 18 people found the following review helpful:
5.0 out of 5 stars
Execllent reference, even for non-statisticians,
By A Customer
This review is from: Matrix Algebra From a Statistician's Perspective (Hardcover)
I am not a statistician, but this book has been my major reference on matrix algebra since I got it. The presentation is a bit dense, but I want to point out that the author actually presents the proofs to essentially _all_ theorems in the book. Perhaps this explains the style. As for the content, I find this book very comprehensive in my experience. But the dense page-setting of the book actually makes it visually challenging to locate a result. I also note that there are extensive exercises at the end of every chapter, although I probably won't use this as a textbook for my students.
17 of 18 people found the following review helpful:
5.0 out of 5 stars
An excellent book on matrices,
By A Customer
This review is from: Matrix Algebra From a Statistician's Perspective (Hardcover)
This book is a true rarity. The exposition is very mathematical, and, therefore, many mathematicians (interested in matrix algebra) will find this book very useful and interesting. The exposition is clear, and quite complete. Of great interest are topics such as idempotent matrices, differentiation of matrices, invertibility.
16 of 19 people found the following review helpful:
5.0 out of 5 stars
Solid and understandable guide to matrix algebra,
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This review is from: Matrix Algebra From a Statistician's Perspective (Hardcover)
I am a PhD level graduate student who has never had a matrix algebra course. I got this book to help with a Linear Models course I am currently taking. The book is very helpful, and provides a solid background in the first few chapters before building on them for more complex results. Definitely a good reference to have nearby.
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Inside This Book
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Key Phrases - Statistically Improbable Phrases (SIPs):
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matrix differentiation, projection matrices, essentially disjoint subspaces, projection matrix with respect, minimum norm generalized inverse, jrth columns, arbitrary generalized inverse, symmetric nonnegative definite matrix, reflexive generalized inverse, firth columns, essential disjointness, nonnull matrices, nonnull matrix, irth rows, nonsingular principal submatrix, symmetric nonnegative definite matrices, matrix whose ijth element, one generalized inverse, unit upper triangular matrix, kjth element, jith element, consistent linear system, nth diagonal elements, essentially immediate consequence, leading principal submatrices Key Phrases - Capitalized Phrases (CAPs): (learn more)
Some Results, Linear Systems, Quadratic Forms, Exercises Section, Some Basic Results, Orthogonal Complements, Second-Degree Polynomial, Inverse Matrices, Cholesky Decompositions, Geometrical Considerations, Some Definitions, The Vech Operator, Use Theorem, Generalize Theorem, Singular Value Decomposition, Some Alternative Characterizations, Recalling Corollary, Form of Solutions, Other Preliminaries, Some Additional Results, Systems of the Form, Ranks of Partitioned Matrices, Constrained Minimization Problem, Partitioned Nonnegative Definite Matrices, Basic Operations Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Surprise Me!
matrix differentiation, projection matrices, essentially disjoint subspaces, projection matrix with respect, minimum norm generalized inverse, jrth columns, arbitrary generalized inverse, symmetric nonnegative definite matrix, reflexive generalized inverse, firth columns, essential disjointness, nonnull matrices, nonnull matrix, irth rows, nonsingular principal submatrix, symmetric nonnegative definite matrices, matrix whose ijth element, one generalized inverse, unit upper triangular matrix, kjth element, jith element, consistent linear system, nth diagonal elements, essentially immediate consequence, leading principal submatrices Key Phrases - Capitalized Phrases (CAPs): (learn more)
Some Results, Linear Systems, Quadratic Forms, Exercises Section, Some Basic Results, Orthogonal Complements, Second-Degree Polynomial, Inverse Matrices, Cholesky Decompositions, Geometrical Considerations, Some Definitions, The Vech Operator, Use Theorem, Generalize Theorem, Singular Value Decomposition, Some Alternative Characterizations, Recalling Corollary, Form of Solutions, Other Preliminaries, Some Additional Results, Systems of the Form, Ranks of Partitioned Matrices, Constrained Minimization Problem, Partitioned Nonnegative Definite Matrices, Basic Operations Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Surprise Me!
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