Matrix Theory and Applications with MATLAB: 1st Edition (Hardback) book cover

Matrix Theory and Applications with MATLAB

1st Edition

By Darald J. Hartfiel

CRC Press

384 pages

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Hardback: 9781584881087
pub: 2000-11-28
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Description

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.

Table of Contents

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

Subject Categories

BISAC Subject Codes/Headings:
MAT002000
MATHEMATICS / Algebra / General
MAT003000
MATHEMATICS / Applied
MAT021000
MATHEMATICS / Number Systems