1st Edition

Basic Matrix Algebra with Algorithms and Applications

By Robert A. Liebler Copyright 2003
    260 Pages 80 B/W Illustrations
    by Chapman & Hall

    260 Pages
    by Chapman & Hall

    264 Pages 80 B/W Illustrations
    by Chapman & Hall

    Clear prose, tight organization, and a wealth of examples and computational techniques make Basic Matrix Algebra with Algorithms and Applications an outstanding introduction to linear algebra. The author designed this treatment specifically for freshman majors in mathematical subjects and upper-level students in natural resources, the social sciences, business, or any discipline that eventually requires an understanding of linear models.

    With extreme pedagogical clarity that avoids abstraction wherever possible, the author emphasizes minimal polynomials and their computation using a Krylov algorithm. The presentation is highly visual and relies heavily on work with a graphing calculator to allow readers to focus on concepts and techniques rather than on tedious arithmetic. Supporting materials, including test preparation Maple worksheets, are available for download from the Internet.

    This unassuming but insightful and remarkably original treatment is organized into bite-sized, clearly stated objectives. It goes well beyond the LACSG recommendations for a first course while still implementing their philosophy and core material. Classroom tested with great success, it prepares readers well for the more advanced studies their fields ultimately will require.

    Recognizing Linear Systems and Solutions
    Matrices, Equivalence and Row Operations
    Echelon Forms and Gaussian Elimination
    Free Variables and General Solutions
    The Vector Form of the General Solution
    Geometric Vectors and Linear Functions
    Polynomial Interpolation
    Complex Numbers
    Matrix Multiplication
    Auxiliary Matrices and Matrix Inverses
    Symmetric Projectors, Resolving Vectors
    Least Squares Approximation
    Changing Plane Coordinates
    The Fast Fourier Transform and the Euclidean Algorithm.
    Eigenvectors and Eigenvalues
    The Minimal Polynomial Algorithm
    Linear Recurrence Relations
    Properties of the Minimal Polynomial
    The Sequence {Ak}
    Discrete dynamical systems
    Matrix compression with components
    Area and Composition of Linear Functions
    Computing Determinants
    Fundamental Properties of Determinants
    Further Applications
    Appendix: The abstract setting
    Selected practice problem answers


    Robert A. Liebler

    "In brief, I think the book is wonderful! … It's pedagogically excellent … The examples are very thoughtfully chosen, anticipating possible misunderstandings and illuminating both the main idea and some subtleties … The emphasis on recursion is unusual and valuable … It's rich in topics not often, if at all, treated effectively in texts at this level … Again, I think this book is terrific …"
    -Harriet Pollatsek, Professor of Mathematics and
    Julia and Sarah Ann Adams Professor of Science,
    Mount Holyoke College, South Hadley, Massachusetts, USA