# A divergence center interpretation of general symmetric Kubo-Ando means, and related weighted multivariate operator means

@article{Pitrik2021ADC, title={A divergence center interpretation of general symmetric Kubo-Ando means, and related weighted multivariate operator means}, author={J. Pitrik and D'aniel Virosztek}, journal={Linear Algebra and its Applications}, year={2021}, volume={609}, pages={203-217} }

Abstract It is well known that special Kubo-Ando operator means admit divergence center interpretations, moreover, they are also mean squared error estimators for certain metrics on positive definite operators. In this paper we give a divergence center interpretation for every symmetric Kubo-Ando mean. This characterization of the symmetric means naturally leads to a definition of weighted and multivariate versions of a large class of symmetric Kubo-Ando means. We study elementary properties of… Expand

#### One Citation

Some notes on quantum Hellinger divergences with Heinz means

- Mathematics
- 2020

The information geometry, convexity, in-betweenness property and the barycenter problem of quantum Hellinger divergences with Heinz means is studied. The limiting cases are also considered.

#### References

SHOWING 1-10 OF 26 REFERENCES

The matrix geometric mean of parameterized, weighted arithmetic and harmonic means

- Mathematics
- 2011

We define a new family of matrix means {Lμ(ω;A)}μ∈R where ω and A vary over all positive probability vectors in Rm and m-tuples of positive definite matrices resp. Each of these means interpolates… Expand

Some Geometric Properties of Matrix Means with respect to Different Distance Function.

- Mathematics
- 2019

In this paper we study the monotonicity, in-betweenness and in-sphere properties of matrix means with respect to Bures-Wasserstein, Hellinger and Log-Determinant metrics. More precisely, we show that… Expand

Transformations on positive definite matrices preserving generalized distance measures

- Mathematics
- 2015

Abstract We substantially extend and unify former results on the structure of surjective isometries of spaces of positive definite matrices obtained in the paper [14] . The isometries there… Expand

Positive definite matrices and the S-divergence

- Mathematics
- 2011

Positive definite matrices abound in a dazzling variety of applications. This ubiquity can be in part attributed to their rich geometric structure: positive definite matrices form a self-dual convex… Expand

Matrix power means and the Karcher mean

- Mathematics
- 2012

We define a new family of matrix means {Pt(ω;A)}t∈[−1,1], where ω and A vary over all positive probability vectors in Rn and n-tuples of positive definite matrices resp. Each of these means except… Expand

Convex multivariate operator means

- Mathematics, Physics
- 2018

Abstract We prove that a trace function, generated by the functional calculus, is geodesically convex in the Riemannian manifold of positive definite matrices, if and only if it is geodesically… Expand

Riemannian geometry and matrix geometric means

- Mathematics
- 2006

The geometric mean of two positive definite matrices has been defined in several ways and studied by several authors, including Pusz and Woronowicz, and Ando. The characterizations by these authors… Expand

In-betweenness, a geometrical monotonicity property for operator means

- Mathematics, Physics
- 2013

Abstract We introduce the notions of in-betweenness and monotonicity with respect to a metric for operator means. These notions can be seen as generalising their natural counterpart for scalar means,… Expand

On the Joint Convexity of the Bregman Divergence of Matrices

- Mathematics, Physics
- 2015

We characterize the functions for which the corresponding Bregman divergence is jointly convex on matrices. As an application of this characterization, we derive a sharp inequality for the quantum… Expand

Matrix analysis

- Computer Science, Mathematics
- 1985

This new edition of the acclaimed text presents results of both classic and recent matrix analyses using canonical forms as a unifying theme, and demonstrates their importance in a variety of applications. Expand