Matrix algebra : an introduction /

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...

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Bibliographic Details
Main Author: Namboodiri, N. Krishnan (Narayanan Krishnan), 1929-2015
Format: Book
Language:English
Published: Beverly Hills : Sage Publications, 1984.
Series:Quantitative applications in the social sciences ; 07-038.
Subjects:
Table of Contents:
  • 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
  • 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.