| | Preface | | |
| | Notation Index | | |
1 | | Vector Spaces and Matrices | | 1 |
1.1 | | Preliminaries | | 1 |
1.2 | | Vector Spaces and Subspaces | | 4 |
1.3 | | Basis and Dimension | | 5 |
1.4 | | Rank | | 8 |
1.5 | | Orthogonality | | 10 |
1.6 | | Nonsingularity | | 14 |
1.7 | | Frobenius Inequality | | 16 |
1.8 | | Eigenvalues and the Spectral Theorem | | 18 |
2 | | Linear Estimation | | 29 |
2.1 | | Generalized Inverses | | 29 |
2.2 | | Linear Model | | 33 |
2.3 | | Estimability | | 35 |
2.4 | | Weighing Designs | | 38 |
2.5 | | Residual Sum of Squares | | 40 |
2.6 | | Estimation Subject to Restrictions | | 42 |
3 | | Tests of Linear Hypotheses | | 51 |
3.1 | | Schur Complements | | 51 |
3.2 | | Multivariate Normal Distribution | | 53 |
3.3 | | Quadratic Forms and Cochrans Theorem | | 57 |
3.4 | | One-Way and Two-Way Classifications | | 61 |
3.5 | | General Linear Hypothesis | | 65 |
3.6 | | Extrema of Quadratic Forms | | 67 |
3.7 | | Multiple Correlation and Regression Models | | 69 |
4 | | Singular Values and Their Applications | | 79 |
4.1 | | Singular Value Decomposition | | 79 |
| | More... | | |