Matrix versions of the Hellinger distance

Rajendra Bhatia, Stephane Gaubert, Tanvi Jain

On the space of positive definite matrices we consider distance functions of the form $d(A,B)=\left[\tr\mathcal{A}(A,B)-\tr\mathcal{G}(A,B)\right]^{1/2},$ where $\mathcal{A}(A,B)$…