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Vectors and Matrices
1st Edition - January 1, 1971
Author: Pamela Liebeck
Editor: C. Plumpton
eBook ISBN:
9 7 8 - 1 - 4 8 3 2 - 8 0 4 3 - 1
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… Read more
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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.
Preface
1 Vectors and Sealars
Introduction
Types of Numbers
Properties of Numbers
Exercise 1a
Vectors
Addition of Vectors
Product of Scalar and Vector
Summary
Exercise 1b
2 The Inner Product
Introduction
Inner Product
Exercise 2a
Position Vectors
The Vector Equation of a Line
The Distributive Property of Inner Product
Summary
Exercise 2b
3 Vectors in Three Dimensions
Introduction
Three-Dimensional Coordinate Vectors
The Vector Product
Points, Lines and Planes
Exercise 3a
The Equations of a Line
The Equation of a Plane-Linear Dependence
Summary
Exercise 3b
4 Geometry Mappings
Introduction
Geometry Mappings
Product of Mappings
Exercise 4a
Linear Mappings
Matrices
Three-Dimensional Mappings
Summary
Exercise 4b
5 Classification of Two by Two Matrices
Introduction
Area and Determinants
Isometric Mappings and Orthogonal Matrices
Many-One Mappings and Singular Matrices
Inverse Mappings and Inverse Matrices
Exercise 5a
Product of Mappings and Product of Matrices
Transpose of a Matrix and Transpose of a Vector
Summary
Exercise 5b
6 Classification of Three by Three Matrices
Introduction
Volume and Determinants
Isometric Mappings and Orthogonal Matrices
Many-One Mappings and Singular Matrices
Inverse Mappings and Inverse Matrices
Exercise 6a
Product of Mappings and Product of Matrices
Transpose of a Matrix and Transpose of a Vector
Summary
Exercise 6b
7 Generalized Vectors and Matrices
Introduction
n-Dimensional Vectors
Polynomials as Vectors
Age Distribution Vectors
Exercise 7a
Rectangular Matrices
Incidence Matrices
Dominance Matrices
Summary
Exercise 7b
8 Linear Equations
Introduction
Elementary Row Operations
Inverse of a Square Matrix
Exercise 8a
Consistent and Inconsistent Equations
The Echelon Form
Calculating Aids
Summary
Exercise 8b
9 Eigenvectors
Introduction
Eigenvectors of a Matrix
The Characteristic Equation
Exercise 9a
Diagonalization
Symmetric Matrices
Summary
Exercise 9b
10 Some Applications of Eigenvectors
Introduction
Quadratic Forms
Exercise 10a
Recurring Processes
Probability
Summary
Outlook
Exercise 10b
Bibliography
Answers to the Exercises
Index
- No. of pages: 192
- Language: English
- Published: January 1, 1971
- Imprint: Pergamon
- eBook ISBN: 9781483280431