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Among the fascinating constructions in mathematics is the Hilbert distance metric on a bounded convex subset of ${\mathbb R}^n$.

Where, within mathematics, is it used ? I know at least a proof of the Perron--Frobenius Theorem for non-negative matrices.

What are its applications in other sciences ?

Among the fascinating constructions in mathematics is the Hilbert distance on a bounded convex subset of ${\mathbb R}^n$.