Communications of the Korean Mathematical Society (대한수학회논문집)
- Volume 9 Issue 3
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- Pages.629-639
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- 1994
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- 1225-1763(pISSN)
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- 2234-3024(eISSN)
ON TRIANGULAR STOCHASTIC MATRICES
Abstract
Loewner ([13]) showend the semigroup of the real non-singular totally positive matrices is generated by itsinfinitesimal elements, that is,s the set of all Jacobi matrices with non-negative off-diagonal elements. In general, a semigroup is not completely recreated from the set of its infinitesimal elements. We extend Loewner's work and show that the semi-group of all invertible upper (or lower) triangular stochastic matrices is generated by the set of its infinitesimal elements.
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