On the Bures-Wasserstein distance between positive definite matrices

@article{Bhatia2017OnTB,
  title={On the Bures-Wasserstein distance between positive definite matrices},
  author={R. Bhatia and Tanvi Jain and Y. Lim},
  journal={arXiv: Functional Analysis},
  year={2017}
}
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 problems, in quantum information and in the theory of optimal transport. It is also related to Riemannian geometry. In the first part of this paper we study this metric from the perspective of matrix analysis, simplifying and unifying various proofs. Then we develop a theory of a mean of two, and a barycentre of several… Expand

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