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 relationship with the orthogonal decomposition.