# matrices – \$PSL(2,mathbb{R})\$, \$PSO(2)\$ and Hyperbolic Distance

Let $$PSL(2,mathbb{R})$$ be the Projective Special Linear Group and $$PSO(2)$$ be the Projective Special Orthogonal Group.

It is well-known that $$PSL(2,mathbb{R})/PSO(2)$$ can be identified with the upper half-plane $$mathbb{H}$$.

Let $$g,h$$ be two elements of $$PSL(2,mathbb{R})$$, How can the hyperbolic distance between $$gPSO(2)$$ and $$hPSO(2)$$ be computed?