- #1

nikozm

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I am puzzled about the following condition. Assume a matrix A with complex-valued zero-mean Gaussian entries and a matrix B with complex-valued zero-mean Gaussian entries too (which are mutually independent of the entries of matrix A).

Then, how can we prove that Trace{[(A*B)^{H}*(A*B)]^{-1}} is always lower that Trace{[(A)^{H}*(A)]^{-1}} ?

The superscripts {H} and {-1} denote the Hermitian transpose and matrix inverse operator, respectively.

Any idea could be helpful.

Thank you very much in advance.