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A theorem on the Gram matrix of a polyhedron

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Abstract

A theorem concerning the Gram matrix of a general set of vectors: a vector polyhedron, is described. Generally speaking, the demonstration is performed by means of a non-negative vector definition: the variance vector, which can be associated to any vector polyhedron belonging to a vector space where a scalar product can be defined. The complete sum of the variance vector, the condensed variance index of any polyhedron, permits to construct the Gram matrix theorem.

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  1. Institut de Química Computacional i Catàlisi, Universitat de Girona, Girona, Catalonia, 17071, Spain

    Ramon Carbó-Dorca

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  1. Ramon Carbó-Dorca
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Correspondence to Ramon Carbó-Dorca.

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Carbó-Dorca, R. A theorem on the Gram matrix of a polyhedron. J Math Chem 55, 79–97 (2017). https://doi.org/10.1007/s10910-016-0672-1

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  • DOI: https://doi.org/10.1007/s10910-016-0672-1

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