On the Bures-Wasserstein distance between positive definite matrices

Rajendra Bhatia, Tanvi Jain, Yongdo Lim

The metric $d(A,B)=\left[ \tr\, A+\tr\, B-2\tr(A^{1/2}BA^{1/2})^{1/2}\right]^{1/2}$ on the manifold of $n\times n$ positive definite matrices arises in various optimisation problem…