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Elementary Linear Algebra with Applications. Third Edition Hardcover – September 8, 1996

ISBN-13: 978-0030103476 ISBN-10: 0030103479 Edition: 3rd

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Product Details

  • Hardcover: 445 pages
  • Publisher: Saunders College Publishing; 3 edition (September 8, 1996)
  • Language: English
  • ISBN-10: 0030103479
  • ISBN-13: 978-0030103476
  • Product Dimensions: 9.7 x 7.8 x 1.1 inches
  • Shipping Weight: 2.7 pounds (View shipping rates and policies)
  • Average Customer Review: 2.2 out of 5 stars  See all reviews (6 customer reviews)
  • Amazon Best Sellers Rank: #776,325 in Books (See Top 100 in Books)

Editorial Reviews

Review

Preface. List of Applications. 1. Introduction to Linear Equations and Matrices. Introduction to Linear Systems and Matrices. Gaussian Elimination. The Algebra of Matrices: Four Descriptions of the Product. Inverses and Elementary Matrices. Gaussian Elimination as a Matrix Factorization. Transposes, Symmetry, and Band Matrices: An Application. Numerical and Programming Considerations: Partial Pivoting, Overwriting Matrices, and Ill-Conditioned Systems. Review Exercises. 2. Determinants. The Determinant Function. Properties of Determinants. Finding det A Using Signed Elementary Products. Cofactor Expansion: Cramer's Rule. Applications. Review Exercises. 3. Vector Spaces. Vectors in 2- and 3-Spaces. Euclidean n-Space. General Vector Spaces. Subspaces, Span, Null Spaces. Linear Independence. Basis and Dimension. The Fundamental Subspaces of a Matrix; Rank. Coordinates and Change of Basis. An Application: Error-Correcting Codes. Review Exercises. Cumulative Review Exercises. 4. Linear Transformations, Orthogonal Projections and Least Squares. Matrices as Linear Transformation. Relationships Involving Inner Products. Least Squares and Orthogonal Projections. Orthogonal Bases and the Gram-Schmidt Process. Orthogonal Matrices, QR Decompositions, and Least Squares (Revisited). Encoding the QR Decompositions: A Geometric Approach. General Matrices of Linear of Linear Transformations; Similarity. Review Exercises. Cumulative Review Exercises. 5. Eigenvectors and Eigenvalues. A Brief Introduction to Determinants. Eigenvalues and Eigenvectors. Diagonalization. Symmetric Matrices. An Application - Difference Equations: Fibonacci Sequences and Markov Processes. An Application -Differential Equations. An Application -- Quadratic Forms. Solving the Eigenvalue Problem Numerically. Review Exercises. Cumulative Review Exercises. 6. Further Directions. Function Spaces. The Singular Value Decomposition -- Generalized Inverses, the General Least-Squares Problem, and an Approach to Ill-Conditioned Systems. Iterative Method. Matrix Norms. General Vector Spaces and Linear Transformations Over an Arbitrary Field. Review Exercises. Appendix A: More on LU Decompositions. Appendix B: Counting Operations and Gauss-Jordan Elimination. Appendix C: Another Application. Appendix D: Introduction to MATLAB and Projects. Bibliography and Further Readings. Index.

Customer Reviews

2.2 out of 5 stars
5 star
17%
4 star
17%
3 star
0%
2 star
0%
1 star
67%
See all 6 customer reviews
I did very well in the class but had to rely heavily on other sources.
Andrew Varamir
I wish that they would do less examples of computation (which is easy enough) and more proofs.
Joanna Lam
I promise that you won't be referencing this book once the semester's over.
Katherine

Most Helpful Customer Reviews

9 of 10 people found the following review helpful By Tony C. on November 24, 2004
Format: Hardcover Verified Purchase
If you are searching for a book to learn the fundamentals of linear algebra, avoid this textbook. I cannot recommend it, and apparently, after almost 20 years in the classroom (it was first published in 1986), neither can anyone else who buys their books from Amazon. If you are required to purchase this book for a class, you are indeed stuck in a tough spot - but help is available...

There are two other books which present linear algebra fundamentals extremely well. You can purchase Anton's Elementary Linear Algebra to help you survive in a class that is using the Hill book. Gilbert Strang's Introduction to Linear Algebra book is also excellent, and employs pragmatic explanations that will clarify the new concepts.

Anton's Elementary Linear Algebra has been around since 1973, is refined, has better diagrams and fuller explanations than the Hill book, and is about the same price. Look at the ratings from readers - four stars plus, based on 11 reviews. Strang's book is brand new (2003), but has already racked up good reviews - Four stars based on 22 reviews...and it is less expensive than the Hill book.

My experience with both the Anton and Strang texts confirm their ratings. I have used both time and time again to help me understand what the Hill book seems to explain poorly, or glosses over completely. Check for yourself...look at the ratings and comments for the Anton and Strang books. The comments are largely positive. Then look at the ratings for the Hill book: as of this writing, there are none. I believe this is not a coincidence, and that this accurately represents a lukewarm reception by Amazon's mathematical readership.

I would bet that Mr. Hill is an excellent instructor in person, but his book is less impressive.
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3 of 3 people found the following review helpful By Joanna Lam on October 3, 2006
Format: Hardcover
This book is not helpful at all. They mostly teach you how to compute and they prove some very basic theorems. Then, the homework asks you to do these complicated proofs that you have no idea how to b/c the text doesn't teach you how. I wish that they would do less examples of computation (which is easy enough) and more proofs. They also have a bad habit of defining key terms within the hw that you might miss.
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2 of 2 people found the following review helpful By Katherine on February 22, 2011
Format: Hardcover Verified Purchase
Unfortunately, I was saddled with this book as a primary, required text in my Linear Algebra course. Richard Hill makes linear algebra unnecessarily difficult.

The examples, although adequate early-on, soon became confusing as the chapters progressed. Many word problems--especially those involving vectors--were written very poorly. Even if I fully understood the concepts of a chapter (having learned the concepts through some means other than this book), I sometimes had to read a question several dozen times before understanding what the problem was even asking. "The vector starting where and with what length? Say what?" Hill clearly hasn't mastered the art of writing mathematical word problems.

The examples and problems in this book also focus more on computation than on application or logic. After reading through a chapter, I'd be able to switch numbers around to achieve a correct answer, but *why* that answer was correct wasn't always clear to me.

Other reviewers seem to agree that, for this book, finding your own supplementary texts is a necessity. For me, the most useful has been Jim Hefferon's Linear Algebra. You can order a paperback copy from Amazon at that link, or you can head to Hefferon's website to download a free .pdf copy, along with loads of practice problems. It's an open (open source?) textbook, but it's of excellent quality--relevant, practical, and clear. Hefferon, unlike Hill, writes with clarity, ease, and purpose!

In short, only buy Hill's book if you absolutely MUST (i.e. it is a required text for your class). Even then, buy the absolute cheapest copy that you can find. I promise that you won't be referencing this book once the semester's over. Otherwise, avoid this book at all costs!
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Elementary Linear Algebra with Applications. Third Edition
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