# Linear Algebra and Linear Models

Springer Science & Business Media, 2000 - Mathematics - 138 pages
The main purpose of Linear Algebra and Linear Modelsis to provide a rigorous introduction to the basic aspects of the theory of linear estimation and hypothesis testing. The necessary prerequisites in matrices, multivariate normal distribution and distributions of quadratic forms are developed along the way. The book is aimed at advanced undergraduate and first-year graduate masters students taking courses in linear algebra, linear models, multivariate analysis, and design of experiments. It should also be of use to research mathematicians and statisticians as a source of standard results and problems.

### What people are saying -Write a review

We haven't found any reviews in the usual places.

### Contents

 Vector Spaces and Matrices 1 12 Vector Spaces and Subspaces 4 13 Basis and Dimension 5 14 Rank 8 15 Orthogonality 10 16 Nonsingularity 14 17 Frobenius Inequality 16 18 Eigenvalues and the Spectral Theorem 18
 38 Exercises 73 39 Hints and Solutions 76 Singular Values and Their Applications 79 42 Extremal Representations 81 43 Majorization 84 44 Principal Components 86 45 Canonical Correlations 88 46 Volume of a Matrix 89

 19 Exercises 22 110 Hints and Solutions 25 Linear Estimation 29 22 Linear Model 33 23 Estimability 35 24 Weighing Designs 38 25 Residual Sum of Squares 40 26 Estimation Subject to Restrictions 42 27 Exercises 46 28 Hints and Solutions 48 Tests of Linear Hypotheses 51 32 Multivariate Normal Distribution 53 33 Quadratic Forms and Cochrans Theorem 57 34 OneWay and TwoWay Classifications 61 35 General Linear Hypothesis 65 36 Extrema of Quadratic Forms 67 37 Multiple Correlation and Regression Models 69
 47 Exercises 93 48 Hints and Solutions 94 Block Designs and Optimality 99 52 The CMatrix 102 53 E A and DOptimality 103 54 Exercises 108 55 Hints and Solutions 110 Rank Additivity 112 62 Characterizations of Rank Additivity 114 63 General Linear Model 118 64 The Star Order 122 65 Exercises 124 66 Hints and Solutions 126 Notes 129 References 132 Index 136 Copyright