1st Edition

Linear Algebra A First Course with Applications

By Larry E. Knop Copyright 2008
    746 Pages 116 B/W Illustrations
    by Chapman & Hall

    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.

    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


    Larry E. Knop

    "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