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# Matrix Algebra

### An Introduction

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

### Paperback

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