# 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.

### Product Details

 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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