Linear images of a normal vector
Proposition taught in Covariance and the multivariate normal, part of Statistical learning
Linear images of a normal vector
| Type | Proposition |
| Taught in | Covariance and the multivariate normal |
| Part | Statistical learning |
Let \mathbf{X}\sim\operatorname{N}_p(\boldsymbol{\mu},\Sigma) with \Sigma of rank p, and let A be an m\times p matrix of rank m\le p. Then \mathbf{Y}=A\mathbf{X} satisfies
\mathbf{Y}\sim\operatorname{N}_m(A\boldsymbol{\mu},\,A\Sigma A^\top).
Used in
- Taught in Covariance and the multivariate normal, where the derivation and examples are.
- All 8 questions on Covariance and the multivariate normal
See also
Affine images of normal vectors · Joint distribution and density · Mean vector and covariance matrix · Correlation · Multivariate normal distribution · Squared Mahalanobis distance · Conditional distribution of a multivariate normal · Partial correlation