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Assume thatHis a n \times m matrix with i.i.d. complex Gaussian entries each with zero mean and variance \sigma. Also, let n>=m. I ' m interested in finding the relation between the distribution ofHHHandHHH, where H stands for the Hermittian transposition. I anticipate that both follow the complex wishart distribution with the same parameters (since they share the same nonzero eigenvalues), but I m not sure about this.

Any ideas ? Thanks in advance..

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# Gram matrix distributions

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