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DUALITY, MONOTONICITY AND THE WIGNER–YANASE–DYSON METRICS

M. R. GRASSELLI

Department of Mathematics and Statistics, McMaster University, Hamilton ON L8S 4K1, Canada

https://doi.org/10.1142/S021902570400161XCited by:8 (Source: Crossref)

Abstract

We show that, for each value of α∈(-1, 1), the only Riemannian metrics on the space of positive definite matrices for which the ∇^(α) and ∇^(-α) connections are mutually dual are matrix multiples of 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:

AMSC: 82C10, 53Z05

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