STRICTLY INFINITESIMALLY GENERATED TOTALLY POSITIVE MATRICES

Let G be a Lie group, let L(G) be its Lie algebra, and let exp : denote the exponential mapping. For , we define the tangent set of S by . We say that a semigroup S is strictly infinitesimally generated if S is the same as the semigroup generated by exp(L(S)). We find a tangent set of the semigroup of all non-singular totally positive matrices and show that the semigroup is strictly infinitesimally generated by the tangent set of the semigroup. This generalizes the familiar relationships between connected Lie subgroups of G and their Lie algebras