Bronson Matrix Methods

An Introduction
1. Auflage 2014
ISBN: 978-1-4832-1661-4
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 300 Seiten, Web PDF

Matrix Methods: An Introduction is a nine-chapter text that emphasizes the methodological aspects of mathematical matrices. This book is intended for an introductory course in matrices similar to those given to sophomore and junior engineering students at Fairleigh Dickinson University. The first five chapters deal with the elementary aspects of matrices, including their definition, determinants, method of inversion, simultaneous linear equations, eigenvalues, and eigenvectors. The remaining chapters explore the materials of fundamental importance to both engineers and scientists. These chapters discuss the principles of matrix calculus, linear differential equations, Jordan canonical forms, and special matrices. A set of exercises is provided at the end of each section, which is basically routine in nature and serves primarily to enhance the reader's ability to use the methods just presented. On occasion, problems are assigned that will extend or complete topics previously introduced. This book is intended primarily for science, engineering, and applied mathematics students.

Richard Bronson is a Professor of Mathematics and Computer Science at Fairleigh Dickinson University and is Senior Executive Assistant to the President. Ph.D., in Mathematics from Stevens Institute of Technology. He has written several books and numerous articles on Mathematics. He has served as Interim Provost of the Metropolitan Campus, and has been Acting Dean of the College of Science and Engineering at the university in New Jersey

Autoren/Hrsg.

Bronson, Richard

Inhaltsverzeichnis

1;Front Cover;1
2;Methods: An Introduction;4
3;Copyright Page;5
4;Table of Contents;8
5;Preface;12
6;Acknowledgments;14
7;CHAPTER 1. MATRICES;18
7.1;1.1 Matrices;18
7.2;1.2 Operations;20
7.3;1.3 Matrix Multiplication—I;22
7.4;1.4 Matrix Multiplication—II;25
7.5;1.5 Special Matrices;30
7.6;1.6 Submatrices and Partitioning;33
7.7;1.7 Vectors;37
8;CHAPTER 2. DETERMINANTS;40
8.1;2.1 Determinants;40
8.2;2.2 Expansion by Cofactors;42
8.3;2.3 Properties of Determinants;46
8.4;2.4 Pivotal Condensation;51
8.5;2.5 Cramer's Rule;54
9;CHAPTER 3. THE INVERSE;58
9.1;3.1 The Inverse;58
9.2;3.2 Simultaneous Equations;62
9.3;3.3 Properties of the Inverse;65
9.4;3.4 Another Method for Inversion;69
9.5;Appendix to Chapter 3;71
10;CHAPTER 4. SIMULTANEOUS LINEAR EQUATIONS;74
10.1;4.1 Linear Systems;74
10.2;4.2 Solutions by Inversion;77
10.3;4.3 Gaussian Elimination;77
10.4;4.4 Linear Independence;81
10.5;4.5 Rank;86
10.6;4.6 Theory of Solutions;92
10.7;4.7 Matrix Solutions;95
10.8;4.8 Homogeneous Systems;98
11;CHAPTER 5. EIGENVALUES AND EIGENVECTORS;101
11.1;5.1 Definitions;101
11.2;5.2 Eigenvalues;103
11.3;5.3 Eigenvectors;107
11.4;5.4 Properties of Eigenvalues and Eigenvectors;111
11.5;5.5 Linearly Independent Eigenvectors;113
12;CHAPTER 6. MATRIX CALCULUS;120
12.1;6.1 Definitions;120
12.2;6.2 Cayley-Hamilton Theorem;124
12.3;6.3 Polynomials of Matrices—Distinct Eigenvalues;127
12.4;6.4 Polynomials of Matrices—General Case;132
12.5;6.5 Functions of a Matrix;136
12.6;6.6 The Function eAt;139
12.7;6.7 Complex Eigenvalues;142
12.8;6.8 Properties of eA;145
12.9;6.9 Derivatives of a Matrix;148
12.10;Appendix to Chapter 6;153
13;CHAPTER 7. LINEAR DIFFERENTIAL EQUATIONS;155
13.1;7.1 Fundamental Form;155
13.2;7.2 Reduction of an nth Order Equation;159
13.3;7.3 Reduction of a System;166
13.4;7.4 Solutions of Systems with Constant Coefficients;170
13.5;7.5 Examples;174
13.6;7.6 Solutions of Systems—General Case;180
13.7;7.7 Properties of the Transition Matrix;184
13.8;7.8 The Adjoint System;188
13.9;Appendix to Chapter 7;191
14;CHAPTER 8. JORDAN CANONICAL FORMS;193
14.1;8.1 Similar Matrices;193
14.2;8.2 Diagonalizable Matrices;196
14.3;8.3 Functions of Matrices—Diagonalizable Matrices;201
14.4;8.4 Generalized Eigenvectors;206
14.5;8.5 Chains;211
14.6;8.6 Canonical Basis;213
14.7;8.7 Jordan Canonical Forms;220
14.8;8.8 Functions of Matrices—General Case;226
14.9;8.9 The Function eAt;233
14.10;Appendix to Chapter 8;235
15;CHAPTER 9. SPECIAL MATRICES;238
15.1;9.1 Introduction;238
15.2;9.2 Inner Products;240
15.3;9.3 Orthonormal Vectors;244
15.4;9.4 Self-Adjoint Matrices;249
15.5;9.5 Real Symmetric Matrices;253
15.6;9.6 Orthogonal Matrices;259
15.7;9.7 Hermitian Matrices;262
15.8;9.8 Unitary Matrices;266
15.9;9.9 Summary;269
15.10;9.10 Positive Definite Matrices;269
16;ANSWERS AND HINTS TO SELECTED PROBLEMS;273
16.1;References;296
17;Index;298