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1st Edition

# Matrix Theory and Applications with MATLAB

By

## Darald J. Hartfiel

ISBN 9781584881087
Published November 28, 2000 by CRC Press
384 Pages

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## Book 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.

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