Revisit on spectral geometric mean
Luyining Gan, Sejong Kim
Abstract
In this paper, we introduce the limit, unique solution of the nonlinear equations, geodesic property, tolerance relations and pinch on the spectral geometric mean for two positive definite operators. We show that the spectral geometric mean is a geodesic with respect to some semi-metric. We also prove that the tolerance relation on determinant one matrices can be characterized by the spectral geometric mean. Moreover, two positive tuples can be pinched by the spectral geometric mean.
Topics & Concepts
GeodesicMathematicsGeometric meanMetric (unit)Weighted geometric meanLimit (mathematics)TupleMathematical analysisPure mathematicsProperty (philosophy)GeometryDiscrete mathematicsPhilosophyEconomicsEpistemologyOperations managementMathematical Inequalities and ApplicationsMathematics and ApplicationsMatrix Theory and Algorithms