Duality, monotonicity and the Wigner-Yanase-Dyson metrics
Mathematical Physics
2007-05-23 v1 Differential Geometry
math.MP
Abstract
We 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.
Keywords
Cite
@article{arxiv.math-ph/0212022,
title = {Duality, monotonicity and the Wigner-Yanase-Dyson metrics},
author = {M. R. Grasselli},
journal= {arXiv preprint arXiv:math-ph/0212022},
year = {2007}
}
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24 pages