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May 7, 2021 at 9:57 comment added Robert Bryant There's a standard formula for the distance function of the $\mathrm{SL}(n,\mathbb{R})$-invariant Riemannian metric on $\mathrm{SL}(n,\mathbb{R})/\mathrm{SO}(n)$. For example, I describe it in my answer mathoverflow.net/questions/108280/…. For $n>2$, to write this distance function explicitly in terms of matrix coefficients appears to be a nontrivial problem.
May 7, 2021 at 8:31 history asked Radu T CC BY-SA 4.0