Suppose I have more observations than I have variables.
E.g. Say 51 variables and 30 observations apiece.

The data matrix is shall we say "wide" (columns correspond
to variables).

The resulting sample covariance matrix on the covariance among
variables is necessarily rank deficient.

Is there anything useful I can learn nevertheless from 
that matrix?  

E.g.:
Is there anything to be garnered from a principle components
decomposition of this covariance matrix in this circumstance?

Thanks -
Ron
.
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