Matrix Algebra: An Introduction / Edition 1

Matrix Algebra: An Introduction / Edition 1

by Krishnan Namboodiri
     
 

ISBN-10: 0803920520

ISBN-13: 9780803920521

Pub. Date: 07/01/1984

Publisher: SAGE Publications

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

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

ISBN-13:
9780803920521
Publisher:
SAGE Publications
Publication date:
07/01/1984
Series:
Quantitative Applications in the Social Sciences Series, #38
Edition description:
New Edition
Pages:
96
Product dimensions:
5.50(w) x 8.50(h) x (d)

Related Subjects

Table of Contents

Series Editor's Introduction5
1.Introduction7
Rectangular Arrays7
Equality of Matrices11
Addition and Subtraction of Matrices12
Multiplication by a Scalar13
Vectors13
Vector Representation of a System of Linear Equations14
Inner Products15
Matrix-Vector Multiplication18
Matrix Multiplication20
Examples of the Use of Matrix Multiplication23
The Identity Matrix26
2.Elementary Operations and the Inverse of a Matrix27
Elementary Operations27
Echelon Matrices31
The Inverse of a Square Matrix33
A Procedure to Calculate the Inverse of a Matrix If It Exists35
Application of the Inverse of a Matrix to the Solution of a System of Equations38
Application in Regression Analysis41
Application in Input-Output Analysis46
3.More About Simultaneous Linear Equations49
Linear Dependence Among a Set of Vectors49
The Rank of a Matrix53
Examples54
Simultaneous Linear Equations55
The Full-Rank Case58
The Less Than Full-Rank Case and the Generalized Inverse59
Homogeneous Equations70
4.Eigenvalues and Eigenvectors74
Determinants74
Eigenvalues and Eigenvectors79
Principal Components88
Symmetric Matrices93
References95
About the Author96

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