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arXiv · 2205.00655

Harmonic Center of an n-Simplex: Some Properties

Vilas Patwardhan
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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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Vilas Patwardhan. 2022-05-02. Harmonic Center of an n-Simplex: Some Properties. https://arxiv.org/abs/2205.00655

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