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Answer by Carlo Beenakker for Expected norm of a product of Gaussian matrices
This follows from the fact that $\mathbb{E}[A^\dagger A]=d I$ (with $A^\dagger$ the conjugate transpose of $A$ and $I$ the $d\times d$ identity matrix)....
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Suppose $C_n$ is a product of $n$$d\times d$ matrices with IID entries coming from standard normal. The following appears to be true. Is there an elementary proof?$$E[\|C_n\|_F^2]=d^{n+1}$$This follows...
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