On the gyrodistance between orthogonal gyrolinear combinations in the Möbius gyrovector space

Abstract

We present a novel identity for norms related to gyroaddition of four elements which satisfy some orthogonal conditions in the Möbius gyrovector space. As an application, we give a concrete and simple procedure to compute the norm  of the Möbius subtraction between two orthogonal gyrolinear combinations consisting of arbitrary finite number of terms, as a counterpart to the classical identity of the norm  of the ordinary subtraction between two ordinary orthogonal linear combinations in a real Hilbert space.