|  |  | 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... |  |  |