An informational divergence geometry for stochastic matrices

Summary The informational divergence between stochastic matrices is not a metric. In this paper we show that, however, consistent definitions can be given of ‘spheres’, ‘segments’ and ‘straight lines’ using the divergence as a sort of ‘distance’ between stochastic matrices. The geometric nature of many ‘reliability functions’ of Information Theory and Mathematical Statistics is thus clarified. This work has been done within the GNIM-CNR research activity.