Fourth Frobenius moment of a pseudo-inverted Gaussian matrix: $\mathbb E\|G^{\dagger}\|_F^4=\frac{r^2(k-r)-2r(r-1)}{(k-r)(k-r-1)(k-r-3)}$

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Fourth Frobenius moment of a pseudo-inverted Gaussian matrix: $\mathbb E\|G^{\dagger}\|_F^4=\frac{r^2(k-r)-2r(r-1)}{(k-r)(k-r-1)(k-r-3)}$ · Prove2Me