For a problem I'm working on, it would be helpful to be able to calculate $E[M M^T]$, where the expectation value is taken over $SL_N(\mathbb{R})$. Is this well defined? I suspect that if it is, the result is a multiple of $I_N$ (sign-flips should kill off-diagonal terms, I think). Is that in fact the case, and if so what is the constant of proportionality?
2026-04-24 23:47:15.1777074435
SL_N(R) quadratic invariant?
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