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Let G be a Lie group, let L(G) be its Lie algebra, and let exp : L(G) ! G denote the exponential mapping. For S µ G, we de¯ne the tangent set of S by L(S) = fX 2 L(G) : exp(tX) 2 S for all t ¸ 0g. We say that a semigroup S is strictly in¯nitesimally generated if S is the same as the semigroup gen- erated by exp(L(S)). We ¯nd a tangent set of the semigroup of all non-singular totally positive matrices and show that the semi-
group is strictly in¯nitesimally generated by the tangent set of the
semigroup. This generalizes the familiar relationships between con-
nected Lie subgroups of G and their Lie algebras
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