Matrix Algebra: An Introduction / Edition 1

by Krishnan Namboodiri

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 , #38
Edition description:	New Edition
Pages:	96
Product dimensions:	5.50(w) x 8.50(h) x (d)

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