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Summary:
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.
References:
[1] I. Chon: Lie group and control theory. Ph.D. thesis at Louisiana state university, 1988.
[2] F. R. Gantmacher: The Theory of Matrices vol. 1 and vol. 2. Chelsea Publ. Comp., New York, 1960. MR 1657129
[3] C. Loewner: On totally positive matrices. Math. Zeitschr. 63 (1955), 338–340. DOI 10.1007/BF01187945 | MR 0073657 | Zbl 0068.25004
[4] C. Loewner: A theorem on the partial order derived from a certain transformation semigroup. Math. Zeitschr. 72 (1959), 53–60. DOI 10.1007/BF01162936 | MR 0107068 | Zbl 0091.26101
[5] H. Min: One parameter semigroups in Lie groups. Master’s thesis at Seoul women’s university, 1995.
[6] V. S. Varadarajan: Lie Groups, Lie Algebras, and Their Representations. SpringerVerlag, New York, 1984. MR 0746308 | Zbl 0955.22500
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