Triangular stochastic matrices generated by infinitesimal elements

Inheung Chon; Hyesung Min

Czechoslovak Mathematical Journal (1999)

  • Volume: 49, Issue: 2, page 249-254
  • ISSN: 0011-4642

Abstract

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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.

How to cite

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Chon, Inheung, and Min, Hyesung. "Triangular stochastic matrices generated by infinitesimal elements." Czechoslovak Mathematical Journal 49.2 (1999): 249-254. <http://eudml.org/doc/30482>.

@article{Chon1999,
abstract = {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.},
author = {Chon, Inheung, Min, Hyesung},
journal = {Czechoslovak Mathematical Journal},
keywords = {Lie group; Lie algebra; triangular stochastic matrix; triangular intensity matrices},
language = {eng},
number = {2},
pages = {249-254},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Triangular stochastic matrices generated by infinitesimal elements},
url = {http://eudml.org/doc/30482},
volume = {49},
year = {1999},
}

TY - JOUR
AU - Chon, Inheung
AU - Min, Hyesung
TI - Triangular stochastic matrices generated by infinitesimal elements
JO - Czechoslovak Mathematical Journal
PY - 1999
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 49
IS - 2
SP - 249
EP - 254
AB - 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.
LA - eng
KW - Lie group; Lie algebra; triangular stochastic matrix; triangular intensity matrices
UR - http://eudml.org/doc/30482
ER -

References

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  1. Lie group and control theory, Ph.D.  thesis at Louisiana state university, 1988. (1988) 
  2. The Theory of Matrices vol. 1 and vol. 2, Chelsea Publ. Comp., New York, 1960. (1960) MR1657129
  3. 10.1007/BF01187945, Math. Zeitschr. 63 (1955), 338–340. (1955) Zbl0068.25004MR0073657DOI10.1007/BF01187945
  4. 10.1007/BF01162936, Math. Zeitschr. 72 (1959), 53–60. (1959) Zbl0091.26101MR0107068DOI10.1007/BF01162936
  5. One parameter semigroups in Lie groups, Master’s thesis at Seoul women’s university, 1995. (1995) 
  6. Lie Groups, Lie Algebras, and Their Representations, SpringerVerlag, New York, 1984. (1984) Zbl0955.22500MR0746308

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