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...
Main Author: | |
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Format: | Book |
Language: | English |
Published: |
Beverly Hills :
Sage Publications,
1984.
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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.