Alternative Formulation
The following version is often seen when considering linear regression. Suppose that is a standard multivariate normal random vector (here denotes the n-by-n identity matrix), and if are all n-by-n symmetric matrices with . Then, on defining, any one of the following conditions implies the other two:
- (thus the are positive semidefinite)
- is independent of for
Read more about this topic: Cochran's Theorem
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