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![]() MIKHAILOV, Mihail. Decomposition of finite pseudometric spaces. In: Mathematical Notes, 1998, vol. 63, pp. 197-204. ISSN 0001-4346. DOI: https://doi.org/10.1007/bf02308759 |
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Mathematical Notes | ||||||
Volumul 63 / 1998 / ISSN 0001-4346 /ISSNe 1573-8876 | ||||||
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DOI:https://doi.org/10.1007/bf02308759 | ||||||
CZU: 515.124 | ||||||
Pag. 197-204 | ||||||
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Here we define decomposable pseudometrics. A pseudometric is decomposable if it can be represented as the sum of two pseudometrics that are obtained in a way other than the multiplication all distances by a positive factor. We consider spaces consisting of n points. We prove that there exist a finite number of indecomposable pseudometrics (that is, a basis) such that any pseudometric is a linear combination of basic pseudometrics with nonnegative coefficients. For n ≤ 7, the basic pseudometrics are listed. A decomposability test is derived for finite pseudometric spaces. We also establish some other conditions of decomposability and indecomposability. |
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Cuvinte-cheie Finite-dimensional krein-millman theorem, Pseudo metric space, Systems of linear equations, Weighted graphs |
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