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Homogeneous and rank bases in spaces of metric configurations

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Abstract

Two families of sets of metric configurations are considered. The conditions are established under which sets from these families are bases for a special linear vector space. It is shown that the transition from the representation of a metric configuration in the trivial basis to its representation in any of the considered bases and back can be effectively calculated. It is shown that the nonnegativity of the decomposition of a metric configuration in the considered bases is a sufficient condition for the semi-metric axioms to hold for this configuration, while the nonnegativity of the decomposition in a rank basis is a necessary and sufficient condition for the metric configuration to have a given rank. The transition coefficients and decomposition components are interpreted in the case of homogeneous bases. Sets from the considered families are indicated that characterize largest-volume cones of metric configurations.

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Authors and Affiliations

  1. Faculty of Computational Mathematics and Cybernetics, Moscow State University, Leninskie gory, Moscow, 119992, Russia

    A. I. Maysuradze

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  1. A. I. Maysuradze
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Original Russian Text © A.I. Maysuradze, 2006, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2006, Vol. 46, No. 2, pp. 344–360.

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Maysuradze, A.I. Homogeneous and rank bases in spaces of metric configurations. Comput. Math. and Math. Phys. 46, 330–344 (2006). https://doi.org/10.1134/S096554250602014X

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  • DOI: https://doi.org/10.1134/S096554250602014X

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