für Mathematik in den Naturwissenschaften Leipzig Dually Flat Manifolds and Global Information Geometry
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چکیده
Dually flat manifolds constitute fundamental mathematical objects of information geometry. This note establishes some facts on the global properties and topology of dually flat manifolds which, in particular, provide answers to questions and problems in global information geometry posed by Amari and Amari-Nagaoka.
منابع مشابه
für Mathematik in den Naturwissenschaften Leipzig Duality versus Dual Flatness in Quantum Information
We investigate questions in quantum information geometry which concern the existence and non-existence of dual and dually flat structures on stratified sets of density operators on finite-dimensional Hilbert spaces. We show that the set of density operators of a given rank admits dually flat connections for which one connection is complete if and only if this rank is maximal. We prove moreover ...
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تاریخ انتشار 2002