Matrix algebra for linear models / Marvin H. J. Gruber.
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TextPublication details: New Jersey : John Wiley, c2014.Description: xv, 375 p. ; 25 cmISBN: - 9781118592557 (cloth)
- 000SA.062 23 G885
| Item type | Current library | Call number | Status | Date due | Barcode | Item holds | |
|---|---|---|---|---|---|---|---|
| Books | ISI Library, Kolkata | 000SA.062 G885 (Browse shelf(Opens below)) | Available | 135594 |
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| 000SA.062 D229 Advances in growth curve models : | 000SA.062 F219 Linear models with R / | 000SA.062 G151 Linear mixed-effects models using R : | 000SA.062 G885 Matrix algebra for linear models / | 000SA.062 H685 Methods and applications of linear models : | 000SA.062 H688 Richly parameterized linear models : | 000SA.062 L744 Linear models of optimal test design / |
Includes bibliographical references (pages 366-367) and index.
1. What Matrices are and Some Basic Operations with Them --
2. Determinants and Solving a System of Equations --
3. The Inverse of a Matrix --
4. Special Matrices and Facts about Matrices that will be Used in the Sequel --
5. Vector Spaces --
6. The Rank of a Matrix and Solutions to Systems of Equations --
7. Finding the Eigenvalues of a Matrix --
8. The Eigenvalues and Eigenvectors of Special Matrices --
9. The Singular Value Decomposition (SVD) --
10. Applications of the Singular Value Decomposition --
11. Relative Eigenvalues and Generalizations of the Singular Value Decomposition --
12. Basic Ideas about Generalized Inverses --
13. Characterizations of Generalized Inverses Using the Singular Value Decomposition --
14. Least Square and Minimum Norm Generalized Inverses --
15. More Representations of Generalized Inverses --
16. Least Square Estimators for Less than Full-Rank Models --
17. Quadratic Forms and their Probability Distributions --
18. Analysis of Variance: Regression Models and the One- and Two-Way Classification --
19. More ANOVA --
20. The General Linear Hypothesis --
21. Unconstrained Optimization Problems --
22. Constrained Minimization Problems with Linear Constraints --
23. The Gauss---Markov Theorem --
24. Ridge Regression-Type Estimators--
Answers to selected exercises--
References--
Index.
A self-contained introduction to matrix analysis theory and applications in the field of statistics Comprehensive in scope, Matrix Algebra for Linear Models offers a succinct summary of matrix theory and its related applications to statistics, especially linear models.
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