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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