1st Edition

Matrix Theory and Applications with MATLAB

By Darald J. Hartfiel Copyright 2001

    Designed for use in a second course on linear algebra, Matrix Theory and Applications with MATLAB covers the basics of the subject-from a review of matrix algebra through vector spaces to matrix calculus and unitary similarity-in a presentation that stresses insight, understanding, and applications. Among its most outstanding features is the integration of MATLAB throughout the text. Each chapter includes a MATLAB subsection that discusses the various commands used to do the computations in that section and offers code for the graphics and some algorithms used in the text.

    All of the material is presented from a matrix point of view with enough rigor for students to learn to compose arguments and proofs and adjust the material to cover other problems. The treatment includes optional subsections covering applications, and the final chapters move beyond basic matrix theory to discuss more advanced topics, such as decompositions, positive definite matrices, graphics, and topology.

    Filled with illustrations, examples, and exercises that reinforce understanding, Matrix Theory and Applications with MATLAB allows readers to experiment and visualize results in a way that no other text does. Its rigor, use of MATLAB, and focus on applications better prepares them to use the material in their future work and research, to extend the material, and perhaps obtain new results of their own.

    REVIEW OF MATRIX ALGEBRA
    Matrices, Systems of Linear Equations, Determinants
    INTRODUCTION TO VECTOR SPACES
    Vector Spaces
    Dimension
    Linear Transformations
    SIMILARITY
    Nonsingular Matrices
    Diagonalization
    Conditions for Diagonalization
    Jordan Forms
    MATRIX CALCULUS
    Calculus of Matrices
    Difference Equations
    Differential Equations
    NORMED VECTOR SPACES
    Vector Norms
    Induced Matrix Norms
    Some Special Norms
    Inner Product Norms and Orthogonality
    UNITARY SIMILARITY
    Unitary Matrices
    Schur Decompositions
    SINGULAR VALUE DECOMPOSITION
    Singular Value Decomposition Theorem
    Applications of the SVD Theorem
    LU AND QR DECOMPOSITIONS
    The LU Decomposition
    The QR Decomposition
    PROPERTIES OF EIGENVALUES AND EIGENVECTORS
    Continuity of Eigenvalues and Eigenvectors
    Perturbation of Eigenvalues and Eigenvectors
    HERMITIAN AND POSITIVE DEFINITE MATRICES
    Positive Definite Matrices
    Special Eigenvalue Results on Hermitian Matrices
    GRAPHICS AND TOPOLOGY
    Two Projection Matrices
    Manifolds and Topological Sets
    APPENDICES
    MATLAB
    Answers to Selected Exercises
    Bibliography

    Biography

    Hartfiel, Darald J.