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Matrix Algebra From a Statistician's Perspective

  • Book
  • © 1997


  • 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"
  • Includes supplementary material:

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About this book

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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Table of contents (23 chapters)


From a review:


"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."


Authors and Affiliations

  • Mathematical Sciences Department, IBM T.J. Watson Research Center, Yorktown Heights, USA

    David A. Harville

About the author

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 spent ten years as a mathematical statistician in the Applied Mathematics Research Laboratory of the Aerospace Research Laboratories (at Wright-Patterson, FB, Ohio, followed by twenty years as a full professor in the Department of Statistics at Iowa State University. He has extensive experience in the area of linear statistical models, having taught (on numberous occasions) M.S.and Ph.D.level courses on that topic,having been the thesis adviser of 10 Ph.D. students,and having authored over 60 research articles. His work has been recognized by his election as a Fellow of the American Statistical Association and the Institute of Mathematical Statistics and as a member of the International Statistical Institute and by his having served as an associate editor of Biometrics and of the Journal of the American Statistical Association.

Bibliographic Information

  • Book Title: Matrix Algebra From a Statistician's Perspective

  • Authors: David A. Harville

  • DOI:

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag New York 1997

  • Softcover ISBN: 978-0-387-78356-7Published: 27 June 2008

  • eBook ISBN: 978-0-387-22677-4Published: 18 April 2006

  • Edition Number: 1

  • Number of Pages: XVI, 634

  • Topics: Statistical Theory and Methods

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