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Matrix Algebra : An Introduction - Krishnan Namboodiri

Matrix Algebra

An Introduction

Paperback Published: 1st August 1984
ISBN: 9780803920521
Number Of Pages: 96

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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.

Series Editor's Introductionp. 5
Introductionp. 7
Rectangular Arraysp. 7
Equality of Matricesp. 11
Addition and Subtraction of Matricesp. 12
Multiplication by a Scalarp. 13
Vectorsp. 13
Vector Representation of a System of Linear Equationsp. 14
Inner Productsp. 15
Matrix-Vector Multiplicationp. 18
Matrix Multiplicationp. 20
Examples of the Use of Matrix Multiplicationp. 23
The Identity Matrixp. 26
Elementary Operations and the Inverse of a Matrixp. 27
Elementary Operationsp. 27
Echelon Matricesp. 31
The Inverse of a Square Matrixp. 33
A Procedure to Calculate the Inverse of a Matrix If It Existsp. 35
Application of the Inverse of a Matrix to the Solution of a System of Equationsp. 38
Application in Regression Analysisp. 41
Application in Input-Output Analysisp. 46
More About Simultaneous Linear Equationsp. 49
Linear Dependence Among a Set of Vectorsp. 49
The Rank of a Matrixp. 53
Examplesp. 54
Simultaneous Linear Equationsp. 55
The Full-Rank Casep. 58
The Less Than Full-Rank Case and the Generalized Inversep. 59
Homogeneous Equationsp. 70
Eigenvalues and Eigenvectorsp. 74
Determinantsp. 74
Eigenvalues and Eigenvectorsp. 79
Principal Componentsp. 88
Symmetric Matricesp. 93
Referencesp. 95
About the Authorp. 96
Table of Contents provided by Syndetics. All Rights Reserved.

ISBN: 9780803920521
ISBN-10: 0803920520
Series: Quantitative Applications in the Social Sciences
Audience: Professional
Format: Paperback
Language: English
Number Of Pages: 96
Published: 1st August 1984
Country of Publication: US
Dimensions (cm): 20.22 x 15.24  x 0.56
Weight (kg): 0.12

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