2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/57231We show that, for each alpha in the interval (-1,1), the only Riemannian metrics on the space of positive definite matrices for which the alpha and -alpha-connections are mutually dual are matrix multiples fo the Wigner-Yanase-Dyson metric. If we further impose that the metric be monotone, then this set is reduced to scalar multiples of the Wigner-Yanase-Dyson metric.24 pagesMathematical PhysicsDifferential Geometry82C10, 53Z05text