Duality, monotonicity and the Wigner-Yanase-Dyson metrics
Duality, monotonicity and the Wigner-Yanase-Dyson metrics
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DOI：
10.1142/s021902570400161x
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发表时间：
2004-06-01
影响因子：
0.9
通讯作者：
Grasselli, MR
中科院分区：
文献类型：
--
作者：
Grasselli, MR
我们证明了，对于每个alpha值都是（-1，1）的元素，正定矩阵空间上del（（alpha））和del（（-alpha））连接相互对偶的唯一黎曼度量是Wigner-Yanase-Dyson度量的矩阵倍数.如果我们进一步强制度量是单调的，那么这个集合被简化为Wigner-Yanase-Dyson度量的标量倍数。
We show that, for each value of alpha is an element of (-1, 1), the only Riemannian metrics on the space of positive definite matrices for which the del((alpha)) and del((-alpha)) 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.