# Relation between covariance and rank

1. Sep 21, 2015

### nikozm

Hi,

Assume a matrix H n\times m, with random complex Gaussian coefficients with zero-mean and unit-variance. The covariance of this matrix (i.e., expectation [HHH]) assuming that m = 1 is lower than another H matrix when m > 1 ??

If this holds, can anyone provide a related reference?