Abstract.
In this paper we consider the convex cone of positive definite matrices as algebraic system equipped with geometric mean and B-loop from the standard matrix polar decomposition. Some algebraic structures of these quasigroups are investigated in the context of matrix theory. In particular, their autotopism groups are completely determined: they are isomorphic to the group of positive real numbers.
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Received: 28 April 2004
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Lim, Y. The geometric mean and B-loop quasigroups of the convex cone of positive definite matrices. Arch. Math. 84, 268–275 (2005). https://doi.org/10.1007/s00013-004-1177-x
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DOI: https://doi.org/10.1007/s00013-004-1177-x