This popular and successful text was originally written for a one-semester course in linear algebra at the sophomore undergraduate level. Consequently, the book deals almost exclusively with real finite dimensional vector spaces, but in a setting and formulation that permits easy generalisation to abstract vector spaces. A wide selection of examples of vector spaces and linear transformation is presented to serve as a testing ground for the theory. In the second edition, a new chapter on Jordan normal form was added which reappears here in expanded form as the second goal of this new edition, after the principal axis theorem. To achieve these goals in one semester it is necessary to follow a straight path, but this is compensated by a wide selection of examples and exercises. In addition, the author includes an introduction to invariant theory to show that linear algebra alone is incapable of solving these canonical forms problems. A compact, but mathematically clean introduction to linear algebra with particular emphasis on topics in abstract algebra, the theory of differential equations, and group representation theory.
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11 of 14 people found the following review helpful:
4.0 out of 5 stars
A very good on linear algebra!,
By Todd Ebert (Long Beach California) - See all my reviews
This review is from: Linear Algebra (Undergraduate Texts in Mathematics) (Hardcover)
I found the book to be very thorough and well written. It seemed very easy to understand except for the chapter on Jordan Canonical Forms. However, I would not recommend this book to someone who is learning it for the first time, unless they have a high degree of mathematical maturity. Try the beginner book by Howard Anton.
1.0 out of 5 stars
Sophomore Level ???,
By
This review is from: Linear Algebra (Undergraduate Texts in Mathematics) (Hardcover)
This book is very confusing. The reader is required to make very large leaps to relate example to exercise. Most of these leaps (chap 2-6) involve wading through set theory instead of applying what was covered in a given chapter. It seems as if the questions are designed so the reader must figure out some "trick" in order to solve the problem. This book may be useful if the reader is very familiar with logic notation, set theory, and linear algebra; otherwise, you will probably spend a lot of time learning these things from other sources.
2 of 6 people found the following review helpful:
1.0 out of 5 stars
A Terrible Textbook,
By
This review is from: Linear Algebra (Undergraduate Texts in Mathematics) (Hardcover)
This book is god-awful. The author will use the same symbol to mean many different things, and won't bother to explain the new terminology if he's used it within the past couple of pages.
It's impossible to open the book and pick the important bits out of each chapter - theorems, proofs, and examples all look the same. If you want to find that theorem you think you saw several pages ago, you have to skim very carefully. The exercises at the end of each chapter are all complete wastes of time. Invert a 5x5 matrix! You won't learn anything useful in the process, but it'll take you a while to get there! If you want to learn linear algebra, just read mathworld and wikipedia instead of buying this book.
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Key Phrases - Statistically Improbable Phrases (SIPs):
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linear transformation whose matrix relative, basis extension theorem, principal axis theorem, nilpotent transformations, associated homogeneous system, ordered bases, reduced echelon form, following linear transformations, inner product space, linearly dependent set, standard orthonormal basis, basis pair, multilinear form, basis for ker, algebraic multiplicity, dimension formula, linearly independent set, cyclic vector, remaining vectors, extension construction, nilpotent matrix, characteristic polynomial, ordered basis, spectral theorem, standard basis New!
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linear transformation whose matrix relative, basis extension theorem, principal axis theorem, nilpotent transformations, associated homogeneous system, ordered bases, reduced echelon form, following linear transformations, inner product space, linearly dependent set, standard orthonormal basis, basis pair, multilinear form, basis for ker, algebraic multiplicity, dimension formula, linearly independent set, cyclic vector, remaining vectors, extension construction, nilpotent matrix, characteristic polynomial, ordered basis, spectral theorem, standard basis New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 84
books:
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100
books
cite this book:
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- Linear Algebra (Oxford Science Publications) by Richard Kaye in Back Matter
- The Heritage of Thales (Undergraduate Texts in Mathematics / Readings in Mathematics) by W.S. Anglin in Front Matter
- Topology of Surfaces (Undergraduate Texts in Mathematics) by L.Christine Kinsey in Back Matter
- Intermediate Calculus (Undergraduate Texts in Mathematics) by Murray H. Protter in Back Matter
- The Mathematics of Nonlinear Programming (Undergraduate Texts in Mathematics) by Anthony L. Peressini in Back Matter
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- Numerical Recipes in Pascal (First Edition): The Art of Scientific Computing by William H. Press on 9 pages
- Discrete Optimization, Volume 11: The State of the Art (Topics in Discrete Mathematics) by E. Boros on page 573, and page 574
- Mathematics for Finance: An Introduction to Financial Engineering (Springer Undergraduate Mathematics Series) by Marek Capinski in Front Matter, and Back Matter
- Algebra and Its Applications (Contemporary Mathematics) by Dinh V. Huynh on page 182, and page 200
- Spatial and Spatiotemporal Econometrics, Volume 18 (Advances in Econometrics) by J. P. LeSage on page 128, and page 161
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