Skip to main content
SpringerLink
Log in

Matrix Algebra: Exercises and Solutions

  • Book
  • © 2001

Overview

Authors:
  1. David A. Harville

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

    View author publications

    You can also search for this author in PubMed   Google Scholar

This is a preview of subscription content, log in via an institution to check access.

Access this book

Log in via an institution
eBook USD 49.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 64.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

Licence this eBook for your library

Institutional subscriptions

Table of contents (22 chapters)

  1. Front Matter

    Pages i-xxxi
    Download chapter PDF

  2. Matrices

    • David A. Harville
    Pages 1-5

  3. Submatrices and Partitioned Matrices

    • David A. Harville
    Pages 7-10

  4. Linear Dependence and Independence

    • David A. Harville
    Pages 11-12

  5. Linear Spaces: Row and Column Spaces

    • David A. Harville
    Pages 13-18

  6. Trace of a (Square) Matrix

    • David A. Harville
    Pages 19-20

  7. Geometrical Considerations

    • David A. Harville
    Pages 21-26

  8. Linear Systems: Consistency and Compatibility

    • David A. Harville
    Pages 27-28

  9. Inverse Matrices

    • David A. Harville
    Pages 29-33

  10. Generalized Inverses

    • David A. Harville
    Pages 35-47

  11. Idempotent Matrices

    • David A. Harville
    Pages 49-54

  12. Linear Systems: Solutions

    • David A. Harville
    Pages 55-61

  13. Projections and Projection Matrices

    • David A. Harville
    Pages 63-67

  14. Determinants

    • David A. Harville
    Pages 69-78

  15. Linear, Bilinear, and Quadratic Forms

    • David A. Harville
    Pages 79-112

  16. Matrix Differentiation

    • David A. Harville
    Pages 113-137

  17. Kronecker Products and the Vec and Vech Operators

    • David A. Harville
    Pages 139-159

  18. Intersections and Sums of Subspaces

    • David A. Harville
    Pages 161-178

  19. Sums (and Differences) of Matrices

    • David A. Harville
    Pages 179-207

  20. Minimization of a Second-Degree Polynomial (in n Variables) Subject to Linear Constraints

    • David A. Harville
    Pages 209-220
Back to top

Keywords

About this book

This book comprises well over three-hundred exercises in matrix algebra and their solutions. The exercises are taken from my earlier book Matrix Algebra From a Statistician's Perspective. They have been restated (as necessary) to make them comprehensible independently of their source. To further insure that the restated exercises have this stand-alone property, I have included in the front matter a section on terminology and another on notation. These sections provide definitions, descriptions, comments, or explanatory material pertaining to certain terms and notational symbols and conventions from Matrix Algebra From a Statistician's Perspective that may be unfamiliar to a nonreader of that book or that may differ in generality or other respects from those to which he/she is accustomed. For example, the section on terminology includes an entry for scalar and one for matrix. These are standard terms, but their use herein (and in Matrix Algebra From a Statistician's Perspective) is restricted to real numbers and to rectangular arrays of real numbers, whereas in various other presentations, a scalar may be a complex number or more generally a member of a field, and a matrix may be a rectangular array of such entities.

Reviews

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. Kräuter, 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." (Jürgen Groß, Statistical Papers, Vol. 43 (4), 2002)

Authors and Affiliations

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

    David A. Harville

Bibliographic Information

  • Book Title: Matrix Algebra: Exercises and Solutions

  • Authors: David A. Harville

  • DOI: https://doi.org/10.1007/978-1-4613-0181-3

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag New York, Inc. 2001

  • Softcover ISBN: 978-0-387-95318-2Published: 06 September 2001

  • eBook ISBN: 978-1-4613-0181-3Published: 27 June 2011

  • Edition Number: 1

  • Number of Pages: XV, 271

  • Number of Illustrations: 1 b/w illustrations

  • Topics: Statistical Theory and Methods

Publish with us

Policies and ethics

Back to top

Search

Navigation