Matrix Algebra: An Introduction / Edition 1

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Overview

Matrix Algebra is a vital tool for mathematics in the social sciences, and yet many social scientists have only a rudimentary grasp of it. This volume serves as a complete introduction to matrix algebra, requiring no background knowledge beyond basic school algebra. Namboodiri's presentation is smooth and readable: it begins with the basic definitions and goes on to explain elementary manipulations and the concept of linear dependence, eigenvalues, and eigenvectors — supplying illustrations through fully-worked examples.

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Product Details

Table of Contents

Series Editor's Introduction 5
1. Introduction 7
Rectangular Arrays 7
Equality of Matrices 11
Addition and Subtraction of Matrices 12
Multiplication by a Scalar 13
Vectors 13
Vector Representation of a System of Linear Equations 14
Inner Products 15
Matrix-Vector Multiplication 18
Matrix Multiplication 20
Examples of the Use of Matrix Multiplication 23
The Identity Matrix 26
2. Elementary Operations and the Inverse of a Matrix 27
Elementary Operations 27
Echelon Matrices 31
The Inverse of a Square Matrix 33
A Procedure to Calculate the Inverse of a Matrix If It Exists 35
Application of the Inverse of a Matrix to the Solution of a System of Equations 38
Application in Regression Analysis 41
Application in Input-Output Analysis 46
3. More About Simultaneous Linear Equations 49
Linear Dependence Among a Set of Vectors 49
The Rank of a Matrix 53
Examples 54
Simultaneous Linear Equations 55
The Full-Rank Case 58
The Less Than Full-Rank Case and the Generalized Inverse 59
Homogeneous Equations 70
4. Eigenvalues and Eigenvectors 74
Determinants 74
Eigenvalues and Eigenvectors 79
Principal Components 88
Symmetric Matrices 93
References 95
About the Author 96
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