Duality, monotonicity and the Wigner-Yanase-Dyson metrics

Details Duality, monotonicity and the Wigner-Yanase-Dyson metrics Duality, monotonicity and the Wigner-Yanase-Dyson metrics

2002-12-05

arxiv.org/abs/math-ph/0212022v1

Physics

Mathematical Physics

24 pages

Scientific paper

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.

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