Decomposition of finite pseudometric spaces |
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Authors: | M. E. Mikhailov |
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Affiliation: | (1) Institute of Genetics, Academy of Sciences of the Republic of Moldova, Kishinev |
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Abstract: | 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 ofn 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. Forn ≤ 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. Translated fromMatematicheskie Zametki, Vol. 63, No. 2, pp. 225–234, February, 1998. |
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Keywords: | pseudo metric space weighted graphs finite-dimensional Krein-Millman theorem systems of linear equations. |
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