gyrovector spaces on the open convex cone of positive de finite matrices
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abstract
in this article we review an algebraic de finition of the gyrogroup and a simpli fied version of the gyrovector space with two fundamental examples on the open ball of finite-dimensional euclidean space, 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 de finite matrices and see 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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mathematics interdisciplinary researchجلد ۱، شماره ۱، صفحات ۱۷۳-۱۸۵
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