Finitely generated gyrovector subspaces and orthogonal gyrodecomposition in the Möbius gyrovector space

In this study, we show that any finitely generated gyrovector subspace in the Möbius gyrovector space coincides with the intersection of the vector subspace generated by the same generators and the Möbius ball. As an application, we present a notion of orthogonal gyrodecomposition and clarify the re...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications 2017-05, Vol.449 (1), p.77-90
Main Authors: Abe, Toshikazu, Watanabe, Keiichi
Format: Article
Language:English
Subjects:
Möbius gyrogroup
Möbius gyrovector space
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Summary:In this study, we show that any finitely generated gyrovector subspace in the Möbius gyrovector space coincides with the intersection of the vector subspace generated by the same generators and the Möbius ball. As an application, we present a notion of orthogonal gyrodecomposition and clarify the relationship with the orthogonal decomposition.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2016.11.039