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I'm investigating the use of optimal transport to define a distance between non-negative matrices that satisfy the condition $\mathbf e^\top\mathbf M\mathbf e = 1$ (i.e., the sum of all elements in ...

I am reading the paper Barycenters in the Wasserstein space by Martial Agueh and Guillaume Carlier. In Proposition 3.5, they prove the existence and uniqueness of $$\nu \mapsto \sum_{i=1}^p \frac{\...