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I have $\boldsymbol{A} = \boldsymbol{G}^H \boldsymbol{G}$ is a Wishart matrix, i.e, $\boldsymbol{G}^H \boldsymbol{G} \sim \mathcal{W}_K (M, \boldsymbol{\Lambda})$ with $\boldsymbol{\Lambda} = \mathrm{diag} (\rho_1, \cdots, \rho_K)$. ($\boldsymbol{G}$ is $M \times K$ matrix ).

We know that $\boldsymbol{B} = (\boldsymbol{G}^H \boldsymbol{G})^{-1}$ is an Inverse Wishart matrix. So how can we calculate the expectation of $\boldsymbol{B}$, i.e, $\mathbb{E} \{\boldsymbol{B}\}$? Thanks!

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