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Articles 1 - 2 of 2
Full-Text Articles in Physical Sciences and Mathematics
Tracing Cyclic Homology Pairings Under Twisting Of Graded Algebras, Sayan Chakraborty, Makoto Yamashita
Tracing Cyclic Homology Pairings Under Twisting Of Graded Algebras, Sayan Chakraborty, Makoto Yamashita
Journal Articles
We give a description of cyclic cohomology and its pairing with K-groups for 2-cocycle deformation of algebras graded over discrete groups. The proof relies on a realization of monodromy for the Gauss–Manin connection on periodic cyclic cohomology in terms of the cup product action of group cohomology.
On The Bures–Wasserstein Distance Between Positive Definite Matrices, Rajendra Bhatia, T. Jain, Yongdo Lim
On The Bures–Wasserstein Distance Between Positive Definite Matrices, Rajendra Bhatia, T. Jain, Yongdo Lim
Journal Articles
The metric d(A,B)=trA+trB−2tr(A1∕2BA1∕2)1∕21∕2 on the manifold of n×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, positive definite matrices with respect to this metric. We explain some recent work on a fixed point iteration for computing this Wasserstein barycentre. Our emphasis is on ideas natural to …