Inequalities and limits of weighted spectral geometric mean
Luyining Gan, Tin-Yau Tam
Abstract
We establish some new properties of spectral geometric mean. In particular, we prove a log majorization relation between (Bts/2A(1−t)sBts/2)1/s and the t-spectral mean A♮tB:=(A−1♯B)tA(A−1♯B)t of two positive semidefinite matrices A and B, where A♯B is the geometric mean, and the t-spectral mean is the dominant one. The limit involving t-spectral mean is also studied. We then extend all the results in the context of symmetric spaces of negative curvature.
Topics & Concepts
MathematicsGeometric meanWeighted geometric meanMajorizationContext (archaeology)Limit (mathematics)CombinatoricsGeneralized meanEigenvalues and eigenvectorsPure mathematicsMathematical analysisGeometryPhysicsPaleontologyBiologyQuantum mechanicsMathematical Inequalities and ApplicationsPoint processes and geometric inequalitiesMathematics and Applications