Special ultrametric matrices and graphs (Q2706244)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Special ultrametric matrices and graphs |
scientific article |
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19 March 2001
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ultrametric matrix
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weighted graph
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M-matrix
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0.8575076
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Special ultrametric matrices and graphs (English)
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\textit{S. Martinez}, \textit{G. Michon} and \textit{J. San Martin} [SIAM J. Matrix Anal. Appl. 15, No. 1, 98-106 (1994; Zbl 0798.15030)] introduced (symmetric) strictly ultrametric matrices and then some authors developed the subject with some variations. The present paper concerns this area. Precisely the author introduces special ultrametric matrices and proves that they are singular and actually limits of convergent sequences of matrices that are inverses of (weakly) diagonally dominant \(M\)-matrices. Furthermore, the author states a characterization of special ultrametric matrices based on weighted trees or paths; he also investigates the non symmetric case and particularly two suitable classes of ultrametric matrices.
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