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Matrix Algebra: An Introduction (Quantitative Applications in the Social Sciences) Paperback – July 1, 1984

ISBN-13: 978-0803920521 ISBN-10: 0803920520

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Product Details

  • Series: Quantitative Applications in the Social Sciences (Book 38)
  • Paperback: 96 pages
  • Publisher: SAGE Publications, Inc (July 1, 1984)
  • Language: English
  • ISBN-10: 0803920520
  • ISBN-13: 978-0803920521
  • Product Dimensions: 5.5 x 0.2 x 8.5 inches
  • Shipping Weight: 4 ounces (View shipping rates and policies)
  • Average Customer Review: 4.2 out of 5 stars  See all reviews (6 customer reviews)
  • Amazon Best Sellers Rank: #164,563 in Books (See Top 100 in Books)

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12 of 14 people found the following review helpful By John M. Ford on September 7, 2010
Format: Paperback
Krishnan Namboodiri sets out to remedy the problem that " science majors and graduate students often fail to go far enough in mathematics to get a thorough grounding in [matrix algebra]." This little green book covers the ground in four chapters and 96 pages.

The author begins by introducing basic matrix concepts and terminology, moving quickly to matrix operations such as addition, multiplication, and inversion. The central concept of linear dependence of sets of matrix rows and matrix columns is then explored, including the implications of this concept for solving simultaneous linear equations. The final chapter introduces the concepts of determinants, eigenvectors and eigenvalues. Applications to principle components analysis are illustrated in the books closing sections.

I read this book as part of a three-week online review course in matrix algebra. Its strengths were the discussion of practical applications and its conciseness. These strengths are counterbalanced by disappointing weaknesses. The dense, formula-driven presentation style made the book hard to follow. A glossary and index would have greatly aided mastery of a large number of new terms and concepts. In the end, I was helped more in the class by free materials I found by searching the web than by this book. I was annoyed that I had purchased it.

After further searching, I became a grateful reader of Charles Cullen's Matrices and Linear Transformations, which is more clear, covers more material, includes numerous practice exercises--and requires less of a little green investment. Save yourself some pain and go directly to Cullen.
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5 of 5 people found the following review helpful By R. Johnson on September 10, 2010
Format: Paperback Verified Purchase
This is a great introduction to matrix algebra. It reads very easily and presents the basics in an intuitive way. While it lacks the dense details and proofs one might want in a more advanced book, it did give me a great framework in which to put those dense details into. I read this in a few days, and found my matrix algebra studies went much better afterward. This is a great investment for anyone preparing for an in depth study of matrix algebra, or anyone wanting to brush up on the basics.
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1 of 1 people found the following review helpful By Professor Niemand on June 30, 2014
Format: Paperback Verified Purchase
The aim of this short book (less than 100 pages) is to enable the reader to rapidly acquire a working knowledge of the key areas of matrix algebra. It could also be useful for a quick review. The emphasis is on those aspects of matrix theory that are of most use in statistics. The good points of the book are clear writing, good examples and freedom from typo's; there is also a short but somewhat dated bibliography. The bad points are the lack of both drill exercises and an index.
Covered theory includes:
Basic matrix operations such as matrix addition, scalar multiplication, matrix multiplication, matrix transposition;
Special types of matrices (square, identity, symmetric, orthogonal, echelon).
A very brief introduction to determinants;
Matrix inversion, including the generalized inverse (a nice touch);
Eigenvalues and eigenvectors (including matrix diagonalization).
(More advanced theory, such as matrices with complex numbers as elements, multilinear forms, the Jordan canonical form, partitioned matrices, etc., are omitted.)
Theorems are sometimes proven, at other times only illustrated.
Illustrative applications include: linear regression, Markov chains, Leontief input-output analysis, solution of systems of linear equations (including the homogeneous and rank-deficient cases), principal components analysis.
The section on principal components analysis is brief, but it gets to the heart of the matter. PCA is an important statistical model reduction technique, making it possible to reduce the number of dimensions of a model, in a way that minimizes loss of accuracy.
The author stresses the importance of centering the data before applying PCA.
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