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Matrix Algebra : Exercises and Solutions - D.A. Harville

Matrix Algebra

Exercises and Solutions

Paperback Published: 6th September 2001
ISBN: 9780387953182
Number Of Pages: 271

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This book contains over 300 exercises and solutions covering a wide variety of topics in matrix algebra. They can be used for independent study or in creating a challenging and stimulating environment that encourages active engagement in the learning process. Thus, the book can be of value to both teachers and students. The requisite background is some previous exposure to matrix algebra of the kind obtained in a first course. The exercises are those from an earlier book by the same author entitled "Matrix Algebra From a Statistician's Perspective". They have been restated (as necessary) to stand alone, and the book includes extensive and detailed summaries of all relevant terminology and notation. The coverage includes topics of special interest and relevance in statistics and related disciplines, as well as standard topics. The overlap with exercises available from other sources is relatively small. David A. Harville is a research staff member in the Mathematical Sciences Department of the IBM T.J. Watson Research Center. Prior to joining the Research Center, he served ten years as a mathematical statistician in the Applied Mathematics Research Laboratory of the Aerospace Research Laboratories at Wright-Patterson Air Force Base, Ohio, followed by twenty years as a full professor in the Department of Statistics at Iowa State University. He has extensive experience in linear statistical models, which is an area of statistics that makes heavy use of matrix algebra, and has taught (on numerous occasions) graduate-level courses on that topic. He has authored over 70 research articles. His work has been recognized by his election as a Fellow of the American Statistical Association and the Institute of Mathematical Statistics.

From the reviews of the first edition:

JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION

..".written as a companion to his earlier book titled MATRIX ALGEBRA FROM A STATISTICIAN'S PERSPECTIVE...this is not just a solutions manual. With 15 pages of definitions and terminology and another 5 pages of notations, the book can be used as an independent reader on advanced topics in linear algebra...when used in conjunction with his earlier book, provides a more in-depth second course on this topic."

"This book collects the exercises from the author's Matrix algebra from a statistician's perspective, (Springer 1997) and includes their solutions. ... It can be used as a stand-alone book with an inspiring collection of exercises ... ." (Adhemar Bultheel, Simon Stevin Bulletin, Vol. 10 (2), 2003)

"The author has collected well over 300 exercises from his earlier book Matrix Algebra From a Statistician's Perspective into a separate volume and he added solutions. The book also contains extensive and detailed summaries of the relevant terminology and notation. ... It will be very useful for any teacher of a linear algebra course as a source of exercises of various levels of difficulty." (European Mathematical Society Newsletter, December, 2003)

"This book comprises well over 300 exercises in (real) matrix algebra and their solutions. ... it represents a valuable resource for any reader trying to gain some practice in the concepts of matrix algebra and looking for suitable exercises accompanied by solutions." (A. Krauter, Internationale Mathematische Nachrichten, Vol. 57 (193), 2003)

"This book is a supplement to the author's previous book (Harville 1997) and contains the solutions to more than three-hundred exercises taken from it. ... This book is especially useful for anyone interested in dealing with proof techniques and tricks concerning matrix algebra. ... For everybody who finds pleasure in reading and learning from Harville's text, this book will have a similar effect and should be viewed as a very useful supplement." (Jurgen GroƟ, Statistical Papers, Vol. 43 (4), 2002)

Preface
Some Notation
Some Terminology
Matricesp. 1
Submatrices and Partitioned Matricesp. 7
Linear Dependence and Independencep. 11
Linear Spaces: Row and Column Spacesp. 13
Trace of a (Square) Matrixp. 19
Geometrical Considerationsp. 21
Linear Systems: Consistency and Compatibilityp. 27
Inverse Matricesp. 29
Generalized Inversesp. 35
Idempotent Matricesp. 49
Linear Systems: Solutionsp. 55
Projections and Projection Matricesp. 63
Determinantsp. 69
Linear, Bilinear, and Quadratic Formsp. 79
Matrix Differentiationp. 113
Kronecker Products and the Vec and Vech Operatorsp. 139
Intersections of Sums of Subspacesp. 161
Sums (and Differences) of Matricesp. 179
Minimization of a Second-Degree Polynomial (in n Variables) Subject to Linear Constraintsp. 209
The Moore-Penrose Inversep. 221
Eigenvalues and Eigenvectorsp. 231
Linear Transformationsp. 251
Referencesp. 265
Indexp. 267
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9780387953182
ISBN-10: 0387953183
Audience: General
Format: Paperback
Language: English
Number Of Pages: 271
Published: 6th September 2001
Publisher: Springer-Verlag New York Inc.
Country of Publication: DE
Dimensions (cm): 23.27 x 15.39  x 1.42
Weight (kg): 0.43

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