STRICTLY INFINITESIMALLY GENERATED TOTALLY POSITIVE MATRICES

Title & Authors
STRICTLY INFINITESIMALLY GENERATED TOTALLY POSITIVE MATRICES
Chon, In-Heung;

Abstract
Let G be a Lie group, let L(G) be its Lie algebra, and let exp : $\small{L(G){\rightarrow}G}$ denote the exponential mapping. For $\small{S{\subseteq}G}$, we define the tangent set of S by $\small{L(S)\;=\;\{X\;{\in}\;L(G)\;:\;exp(tX)\;\in\;S\;for\;all\;t\;{\geq}\;0\}}$. We say that a semigroup S is strictly infinitesimally generated if S is the same as the semigroup generated by exp(L(S)). We find a tangent set of the semigroup of all non-singular totally positive matrices and show that the semigroup is strictly infinitesimally generated by the tangent set of the semigroup. This generalizes the familiar relationships between connected Lie subgroups of G and their Lie algebrasᆘﾖ⨀ጊ㴀Ѐ㘶㐻Ԁ䭃䑎䷙ᜊ؀Íᜒ৬6㘴Ԁ䭃䑎䴀
Keywords
tangent cone;infinitesimally generated;totally positive matrix;Jacobi matrix;
Language
English
Cited by
References
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