Liebeck / Plumpton Vectors and Matrices

1. Auflage 2014
ISBN: 978-1-4832-8043-1
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 192 Seiten, Web PDF

Vectors and Matrices provides a progressive approach to vectors and matrices. The first half of this book is devoted to geometry, introducing matrices through its association with geometry mappings, while the rest of the chapters focus on the importance of matrices in non-geometric situations, such as the theory of linear equations and eigenvector theory. The power of eigenvector theory and its application to some problems in biology, probability, and genetics are also reviewed. Other topics include the product of scalar and vector, vector equation of a line, linear dependence, three-dimensional mappings, and orthogonal matrices. The transpose of a matrix and vector, rectangular matrices, inverse of a square matrix, and eigenvectors of a matrix are likewise emphasized in this text. This publication is beneficial to students and researchers conducting work on vectors and matrices.

Autoren/Hrsg.

Liebeck, Pamela

Plumpton, C.

Inhaltsverzeichnis

1;Front Cover;1
2;Vectors and Matrices;4
3;Copyright Page;5
4;Table of Contents;6
5;PREFACE;8
6;CHAPTER 1. VECTORS AND SCALARS;10
6.1;Introduction;10
6.2;Types of Numbers;10
6.3;Properties of Numbers;11
6.4;Exercise 1a;12
6.5;Vectors;13
6.6;Addition of Vectors;14
6.7;Product of Scalar and Vector;19
6.8;Summary of Chapter 1;22
6.9;Exercise 1b;22
7;CHAPTER 2. THE INNER PRODUCT;24
7.1;Introduction;24
7.2;Inner Product;25
7.3;Exercise 2a;31
7.4;The Vector Equation of a Line;34
7.5;The Distributive Property of Inner Product;38
7.6;Summary of Chapter 2;39
7.7;Exercise 2b;40
8;CHAPTER 3. VECTORS IN THREE DIMENSIONS;41
8.1;Introduction;41
8.2;Three-dimensional Coordinate Vectors;42
8.3;Points, Lines and Planes;50
8.4;Exercise 3a;52
8.5;The Equations of a Line;52
8.6;The Equation of a Plane;55
8.7;Linear Dependence;59
8.8;Summary of Chapter 3;61
8.9;Exercise 3b;61
9;CHAPTER 4. GEOMETRY MAPPINGS;63
9.1;Introduction;63
9.2;Geometry Mappings;65
9.3;Product of Mappings;70
9.4;Exercise 4a;72
9.5;Linear Mappings;73
9.6;Matrices;74
9.7;Three-dimensional Mappings;80
9.8;Summary of Chapter 4;85
9.9;Exercise 4b;85
10;CHAPTER 5. CLASSIFICATION OF TWO BY TWO MATRICES;87
10.1;Introduction;87
10.2;Area and Determinants;88
10.3;Isometric Mappings and Orthogonal Matrices;89
10.4;Many–One Mappings and Singular Matrices;91
10.5;Inverse Mappings and Inverse Matrices;92
10.6;Product of Mappings and Product of Matrices;94
10.7;Transpose of a Matrix and Transpose of a Vector;97
10.8;Exercise 5b;101
11;CHAPTER 6. CLASSIFICATION OF THREE BY THREE MATRICES;103
11.1;Introduction;103
11.2;Volume and Determinants;104
11.3;Isometric Mappings and Orthogonal Matrices;106
11.4;Many–One Mappings and Singular Matrices;108
11.5;Inverse Mappings and Inverse Matrices;109
11.6;Exercise 6a;110
11.7;Product of Mappings and Product of Matrices;111
11.8;Transpose of a Matrix and Transpose of a Vector;112
11.9;Summary of Chapter 6;114
11.10;Exercise 6b;114
12;CHAPTER 7. GENERALISED VECTORS AND MATRICES;116
12.1;Introduction;116
12.2;Polynomials as Vectors;119
12.3;Age Distribution Vectors;120
12.4;Exercise 7a;121
12.5;Rectangular Matrices;122
12.6;Incidence Matrices;124
12.7;Dominance Matrices;126
12.8;Summary of Chapter 7;128
13;CHAPTER 8. LINEAR EQUATIONS;130
13.1;Introduction;130
13.2;Elementary Row Operations;131
13.3;Inverse of a Square Matrix;133
13.4;Exercise 8a;137
13.5;Consistent and Inconsistent Equations;138
13.6;The Echelon Form;139
13.7;Calculating Aids;145
13.8;Summary of Chapter 8;146
14;CHAPTER 9. EIGENVECTORS;149
14.1;Introduction;149
14.2;Eigenvectors of a Matrix;150
14.3;The Characteristic Equation;153
14.4;Exercise 9a;157
14.5;Diagonalisation;158
14.6;Symmetric Matrices;161
14.7;Summary of Chapter 9;164
14.8;Exercise 9b;164
15;CHAPTER 10. SOME APPLICATIONS OF EIGENVECTORS;166
15.1;Introduction;166
15.2;Quadratic Forms;166
15.3;Exercise 10a;171
15.4;Recurring Processes;172
15.5;Probability;175
15.6;Summary of Chapter 10;180
15.7;Outlook;181
15.8;Exercise 10b;181
16;BIBLIOGRAPHY;183
17;ANSWERS TO THE EXERCISES;184
18;INDEX;191