We show that each element in the semigroup $S_n$ of all $n \times n$ non-singular upper (or lower) triangular stochastic matrices is generated by the infinitesimal elements of $S_n$, which form a cone consisting of all $n \times n$ upper (or lower) triangular intensity matrices.
 I. Chon: Lie group and control theory. Ph.D. thesis at Louisiana state university, 1988.
 F. R. Gantmacher: The Theory of Matrices vol. 1 and vol. 2
. Chelsea Publ. Comp., New York, 1960. MR 1657129
 H. Min: One parameter semigroups in Lie groups. Master’s thesis at Seoul women’s university, 1995.
 V. S. Varadarajan: Lie Groups, Lie Algebras, and Their Representations
. SpringerVerlag, New York, 1984. MR 0746308
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