Vectors and Matrices

Vectors and Matrices

1st Edition - January 1, 1971

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  • Author: Pamela Liebeck
  • eBook ISBN: 9781483280431

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Description

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.

Table of Contents


  • 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

Product details

  • No. of pages: 192
  • Language: English
  • Copyright: © Pergamon 1971
  • Published: January 1, 1971
  • Imprint: Pergamon
  • eBook ISBN: 9781483280431

About the Author

Pamela Liebeck

About the Editor

C. Plumpton

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