- Hardcover: 445 pages
- Publisher: Saunders College Publishing; 3 edition (September 8, 1996)
- Language: English
- ISBN-10: 0030103479
- ISBN-13: 978-0030103476
- Product Dimensions: 7.8 x 1.1 x 9.7 inches
- Shipping Weight: 1.6 pounds
- Average Customer Review: 13 customer reviews
- Amazon Best Sellers Rank: #450,788 in Books (See Top 100 in Books)
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Elementary Linear Algebra with Applications. Third Edition 3rd Edition
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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.
About the Author
Julia Butterfly Hill, twenty-six, is a writer, a poet, and an activist. She helped found the Circle of Life Foundation to promote the sustainability, restoration, and preservation of life. The foundation is sponsored by the nonprofit Trees Foundation, which works toward the conservation and preservation of forest ecosystems. Hill has been the recipient of many honors and awards, and is a frequent speaker for environmental conferences around the world.
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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!
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. Those who helped him write it have let him down. If you are a student or colleague of Mr. Hill, and you feel differently than I do, then I encourage you to post a review in favor of his textbook.
As a final note, "3D Math Primer for Graphics and Game Development" by Fletcher Dunn and Ian Parberry provides some excellent auxillary material on how computer science and simulation programmers will be using vectors and matrices. Great pictures, diagrams, and explanations. It will help you see why you are learning this linear algebra stuff, and how to begin applying it in your career field. It has high ratings from it's readers at Amazon, and for good reason.
If this book is required, cry and then go get a supplement, then pray that your teacher doesn't suck. Otherwise you will be struggling through a subject that isn't as complicated as this book makes it out to be.