Contents

• 1.1. Vector Spaces

• 1.2. Linear Transformations

• 1.3. Inner Product Spaces

• 1.4. The Cauchy-Schwarz Inequality

• 1.5. The Space $\Lambda (V,W)$

• 1.6. Determinants and Eigenvalues

• 1.7. The Spectral Theorem

• Problems

• Notes and References

Contents

• 2.1. Random Vectors

• 2.2. Independence of Random Vectors

• 2.3. Special Covariance Structures

• Problems

• Notes and References

Contents

• 3.1. The Normal Distribution

• 3.2. Quadratic Forms

• 3.3. Independence of Quadratic Forms

• 3.4. Conditional Distributions

• 3.5. The Density of the Normal Distribution

• Problems

• Notes and References

Contents

• 4.1. The Classical Linear Model

• 4.2. More About the Gauss-Markov Theorem

• 4.3. Generalized Linear Models

• Problems

• Notes and References

Contents

• 5.1. Matrix Factorizations

• 5.2. Jacobians

• Problems

• Notes and References

Contents

• 6.1. Groups

• 6.2. Invariant Measures and Integrals

• 6.3. Invariant Measures on Quotient Spaces

• 6.4. Transformations and Factorizations of Measures

• Problems

• Notes and References

Contents

• 7.1. Left $O_n$ Invariant Distributions on $n$ x p$ Matrices

• 7.2. Groups Acting on Sets

• 7.3. Invariant Probability Models

• 7.4. The Invariance of Likelihood Methods

• 7.5. Distribution Theory and Invariance

• 7.6. Independence and Invariance

• Problems

• Notes and References

Contents

• 8.1. Basic Properties

• 8.2. Partitioning a Wishart Matrix

• 8.3. The Noncentral Wishart Distribution

• 8.4. Distributions Related to Likelihood Ratio Tests

• Problems

• Notes and References

Contents

• 9.1. The MANOVA Model

• 9.2. MANOVA Problems with Block Diagonal Covariance Structure

• 9.3. Intraclass Covariance Structure

• 9.4. Symmetry Models: An Example

• 9.5. Complex Covariance Structures

• 9.6. Additional Examples of Linear Models

• Problems

• Notes and References

Contents

• 10.1. Population Canonical Correlation Coefficients

• 10.2. Sample Canonical Correlations

• 10.3. Some Distribution Theory

• 10.4. Testing for Independence

• 10.5. Multivariate Regression

• Problems

• Notes and References