The sample covariance of paired observations 
for 
is commonly defined by
 |
where 
and 
are the two sample means. With independent observations
from a population having finite second moments, this
denominator makes 
an unbiased estimator of the population covariance.
Using denominator 
instead gives the second mixed sample central
moment and is also called sample covariance by some authors. The convention must
therefore be stated. Collecting the pairwise sample covariances of a random sample
of vectors gives the sample covariance matrix.
