Linear Algebra. Pure and Applied Mathematics

By Peter D. Lax

Book Overview

This introduction to linear algebra by world-renowned mathematician Peter Lax is unique in its emphasis on the analytical aspects of the subject as well as its numerous applications. The book grew out of Dr. Lax's course notes for the linear algebra classes he teaches at New York University. Geared to graduate students as well as advanced undergraduates, it assumes only limited knowledge of linear algebra and avoids subjects already heavily treated in other textbooks. And while it discusses linear equations, matrices, determinants, and vector spaces, it also in-cludes a number of exciting topics that are not covered elsewhere, such as eigenvalues, the Hahn-Banach theorem, geometry, game theory, and numerical analysis. The first four chapters are devoted to the abstract structure of finite dimensional vector spaces. Subsequent chapters deal with determinants as a blend of geometry, algebra, and general spectral theory. Euclidean structure is used to explain the notion of selfadjoint mappings and their spectral theory. Dr. Lax moves on to the calculus of vector and matrix valued functions of a single variable--a neglected topic in most undergraduate programs--and presents matrix inequalities from a variety of perspectives. Fundamentals--including duality, linear mappings, and matrices Determinant, trace, and spectral theory Euclidean structure and the spectral theory of selfadjoint maps Calculus of vector and matrix valued functions Matrix inequalities Kinematics and dynamics Convexity and the duality theorem Normed linear spaces, linear mappings between normed spaces, and positive matrices Iterative methods for solving systems of linear equations Eight appendices devoted to important related topics, including special determinants, Pfaff's theorem, symplectic matrices, tensor product, lattices, fast matrix multiplication, Gershgorin's theorem, and multiplicity of eigenvalues Later chapters cover convexity and the duality theorem, describe the basics of normed linear spaces and linear maps between normed spaces, and discuss the dominant eigenvalue of matrices whose entries are positive or merely non-negative. The final chapter is devoted to numerical methods and describes Lanczos' procedure for inverting a symmetric, positive definite matrix. Eight appendices cover important topics that do not fit into the main thread of the book. Clear, concise, and superbly organized, Linear Algebra is an excellent text for advanced undergraduate and graduate courses and also serves as a handy professional reference.

• Format: Hardcover
• Language: English
• ISBN: 0471111112
• ISBN13: 9780471111115
• Release Date: January 1997
• Publisher: Wiley-Interscience
• Length: 250 Pages
• Weight: 1.35 lbs.
• Dimensions: 9.4" x 0.7" x 6.3"

Customer Reviews

concise and elegant, and also covers Banach spaces

I would compare this book with Paul Halmos' classic "Finite Dimensional Vector Spaces". Both books cover much in common, both in material and style. Each is slender and gracefully written. Lax takes us through many of the simple results and methods of linear algebra. Unlike Halmos, this book also covers computational aspects. A nod to the ever increasing prevalence of computers. The theorems are proven in a rigorous fashion. But with some attention, you should be able to follow the logic. Lax also provides a discussion of Banach spaces - complete normed spaces. Whereas other linear algebra texts might focus more on Hilbert spaces, which are complete inner product spaces. The inner product is bilinear, which leads to easier analysis than for normed spaces. Which is perhaps why Banach spaces are typically not as well covered.

Excellent Graduate Presentation of Linear Algebra

I used to hate this book but it was due to inadequate presentation at the time I was first introduced to it. Over time it has become my favorite Linear Algebra text. Use Axler's "Linear Algebra Done Right" then move up to this text. Being able to do linear algebra at this level is crucial to anyone doing advanced mathematics, science, and engineering. Be sure to have it handy.

My first math book without picturse and examples

I used Lax in my honor linear algebra class as a college freshman. With not much previous experience in abstract math, this book could be a bit frustrating. However, if you really strive to understand what each sentence really means, it's not all that difficult. This is a very concise book and at times I spent hours reading one page. My class didn't end up covering the whole book, but I finished it on my own the summer following my freshman year. Now I feel very confident about linear algebra and it led to my later more in-depth study in algebra.

Best Linear Algebra Review Book

Linear Algebra is one of the most basic topics in science and engineering. Everyone takes an undergraduate course, but few science/engineering graduate students have mastery of the material upon entering grad school. I find that Lax's book is an excellent book to recommend to our graduate students for self review. The few but very well chosen topics and the straightforward yet deep way they are covered make the book engaging, thought provoking, and easily followed by upper level undergrads and beginning grad students. A student with a mastery of the material in this book will have little trouble with grad courses in the many engineering and science courses that rely on linear algebra.