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
1 Citations
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References

SHOWING 1-10 OF 26 REFERENCES
The matrix geometric mean of parameterized, weighted arithmetic and harmonic means
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 interpolatesExpand
Some Geometric Properties of Matrix Means with respect to Different Distance Function.
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 thatExpand
Transformations on positive definite matrices preserving generalized distance measures
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 thereExpand
Positive definite matrices and the S-divergence
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 convexExpand
Matrix power means and the Karcher mean
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 exceptExpand
Convex multivariate operator means
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 geodesicallyExpand
Riemannian geometry and matrix geometric means
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 authorsExpand
In-betweenness, a geometrical monotonicity property for operator means
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
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 quantumExpand
Matrix analysis
TLDR
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
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