Gyrovector Spaces on the Open Convex Cone of Positive Definite Matrices

Document Type : Special Issue: AIMC 51

Author

Department of Mathematics, Chungbuk National University, Cheongju 28644, Korea

Abstract

‎In this article we review an algebraic definition of the gyrogroup and a simplified version of the gyrovector space with two fundamental examples on the open ball of finite-dimensional Euclidean spaces‎, ‎which are the Einstein and Möbius gyrovector spaces‎. ‎We introduce the structure of gyrovector space and the gyroline on the open convex cone of positive definite matrices and explore its interesting applications on the set of invertible density matrices‎. ‎Finally we give an example of the gyrovector space on the unit ball of Hermitian matrices‎. 

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References

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Mathematics Interdisciplinary Research
Volume 1, Issue 1 - Serial Number 1
January 2016
Pages 173-185

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