Harmonic Center of an n-Simplex: Some Properties
Metric Geometry
2022-05-03 v1
Abstract
A simplex in n dimensions is defined by the usual (n+1) linear inequality constraints in n dimensions. Here we consider simplexes which are bounded sets. The harmonic center has been defined earlier for polytopes in general. A relationship between the rows of A is derived here, which must be satisfied for the simplex to be bounded. Using this condition, an interesting relationship is derived between the (n+1) residuals at the harmonic center of the simplex. Finally, a linear expression is developed which is invariant everywhere in the simplex.
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Cite
@article{arxiv.2205.00655,
title = {Harmonic Center of an n-Simplex: Some Properties},
author = {Vilas Patwardhan},
journal= {arXiv preprint arXiv:2205.00655},
year = {2022}
}
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7 pages