Covariance
by pxlogpx
Covariance is defined, for two random variables, as the formula
If we have quantum variable, the definition becomes
. If we have a set of random variables, say , a covariance matrix can be defined, , where
Now the interesting thing is that the covariance matrix is positive.
Proof:
Since
Given any column vector , we have
where .
Since u is any vector, V must be positive.