1st Edition

Linear Algebra
A First Course with Applications

ISBN 9781584887829
Published August 28, 2008 by Chapman and Hall/CRC
752 Pages 116 B/W Illustrations

USD $150.00

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Book Description

Linear Algebra: A First Course with Applications explores the fundamental ideas of linear algebra, including vector spaces, subspaces, basis, span, linear independence, linear transformation, eigenvalues, and eigenvectors, as well as a variety of applications, from inventories to graphics to Google’s PageRank.

Unlike other texts on the subject, this classroom-tested book gives students enough time to absorb the material by focusing on vector spaces early on and using computational sections as numerical interludes. It offers introductions to Maple™, MATLAB®, and TI-83 Plus for calculating matrix inverses, determinants, eigenvalues, and eigenvectors.

Moving from the specific to the general, the author raises questions, provides motivation, and discusses strategy before presenting answers. Discussions of motivation and strategy include content and context to help students learn.

Table of Contents

Preface for the Instructor
A Little Logic
Logical Foundations
Logical Equivalences
Sets and Set Notation
An Introduction to Vector Spaces
The Vector Space R2—The Basics
The Vector Space R2—Beyond the Basics
The Vector Spaces Rn—The Basics
The Vector Spaces Rn—Beyond the Basics
The Vector Spaces Rn—Lines and Planes
Vector Spaces in General
Vector Spaces: Setting the Rules
Vector Spaces: On the Wild Side
Subspaces and Linear Equations
Subspaces from Subsets
A Numerical Interlude—Systems of Linear Equations
Solving Linear Systems
Systematic Solutions of Systems
Technology and Linear Algebra
The Structure of Vector Spaces
Spanning Sets
Linear Independence
More on Linear Independence
Linear Independence and Span
Vector Space Bases
The Dimension of a Vector Space
Linear Transformations
Transformation Fundamentals
Vector Space Isomorphisms
Linear Transformations and Matrices
Matrix Representations of Transformations
Matrices and Associated Vector Spaces
Inverses in Matrix Multiplication
Elementary Matrices
An Introduction to Determinants
Properties of Determinants
Eigenvalues and Eigenvectors
Eigenvalues, Eigenvectors, and Eigenspaces
More on Eigenvalues, Eigenvectors, and Eigenspaces
Forests, Digraphs, and PageRank
Answers to Selected Problems

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"Knop (Hamilton College) speaks directly to undergraduates with the intention of not only teaching concepts and skills pertaining to the field of linear algebra, but also encouraging them to read mathematics . . . Most importantly, perhaps, is the author saw a positive response in his students’ performance in linear algebra when this book was used in his class."

– J.T. Zerger, Catawba College, in Choice: Current Reviews for Academic Libraries, August 2009, Vol. 46, No. 11


"To summarize, by limiting the mathematical scope of the book, and by carefully smoothing the path from the particular to the general, the author has provided an alternative approach to linear algebra that will be of interest to many of those who currently teach it."

– Peter Ruane, in MAA Online, February 2009