Extends the t-geometric mean for positive definite matrices to symmetric spaces, suggesting geometric connections.
The concept of the t -geometric mean of two positive definite matrices is extended to symmetric spaces of noncompact type.The t -geometric mean of two points in such a symmetric space yields the unique geodesic joining the points and the geometric mean is the midpoint.A parametrization of the geodesic in terms of the two points is given.Inequalities about geometric mean and geodesic triangle are given in terms of Kostant's pre-order on semisimple Lie groups as well as on their Lie algebras.
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Liao et al. (2014) studied this question.
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