Relation between covariance and rank

nikozm
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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?

Thanks in advance
 
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What does HHH mean? HHT?

How do you compare two covariance matrices to say which one is "lower"?
 

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