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Random Vectors and Random Matrices
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Classroom Contents
General Linear Models - Background Material
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- 1 Random Vectors and Random Matrices
- 2 Statistical Distributions: Central & Noncentral t Distributions
- 3 Statistical Distributions: Central & Noncentral Chi square df=1 Distributions
- 4 Statistical Distributions: Derive the F Distribution
- 5 Statistical Distributions: NonCentral F Distribution
- 6 Idempotent Matrices
- 7 Independence of Quadratic Forms
- 8 Independence of Quadratic Forms (another proof)
- 9 Distribution of quadratic form n(xbar-mu)Sigma(xbar-mu), where x~MVN(mu,sigma)
- 10 Distribution of Quadratic Forms (part 1)
- 11 Distribution of Quadratic Forms (part 2)
- 12 Distribution of Quadratic Forms (part 3)
- 13 (1-a)% Confidence Region for a multivariate mean vector when the data are multivariate normal
- 14 Derivative of a Quadratic Form with respect to a Vector
- 15 Projection Matrices: Introduction
- 16 Perpendicular Projection Matrix
- 17 Mean, Variance, and Covariance of Quadratic Forms
- 18 A Square-Root Matrix
- 19 Inverse of a Partitioned Matrix
- 20 The Spectral Decomposition (Eigendecomposition)
- 21 Woodbury Matrix Identity & Sherman-Morrison Formula
- 22 Generalized Inverse Matrix
- 23 Generalized Inverse for a Symmetric Matrix
- 24 Gram-Schmidt Orthonormalization Process: Perpendicular Projection Matrix
- 25 Sum of Perpendicular Projection Matrices
