While it is a statistical distance, it is not a metric, the most familiar type of distance, but instead it is a divergence. While metrics are symmetric and generalize linear distance, satisfying the triangle inequality, divergences are asymmetric and generalize squared distance, in some cases satisfying a generalized Pythagorean theorem. In general D KL ( P ∥ ∥ Q ) does not equal D KL ( Q ∥ ∥ P ) , and the asymmetry is an important part of the geometry. The infinitesimal form of relative entropy, specifically its Hessian, gives a metric tensor that equals the Fisher information metric ; see § Fisher information metric. Relative entropy satisfies a generalized Pythagorean theorem for exponential families (geometrically interpreted as dually flat manifolds), and this allows one to minimize relative entropy by geometric means, for example by information projection and in maximum likelihood estimation.