Relation between covariance and rank

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SUMMARY

The discussion centers on the covariance of a matrix H with random complex Gaussian coefficients, specifically comparing the covariance when m = 1 versus m > 1. It is established that the covariance matrix, represented as E[HHH], is lower for the case of m = 1. Participants seek clarification on the notation HHH and HHT, as well as methods for comparing covariance matrices to determine which is lower.

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  • Basic concepts of linear algebra
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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
 
Physics news on Phys.org
What does HHH mean? HHT?

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

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