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Graph of Ultrametric Type Matrices

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Part of the Lecture Notes in Mathematics book series (LNM,volume 2118)

Abstract

Ultrametric and GUM matrices can be seen as the potential matrices of Markov chains on finite state spaces. In this chapter we study the connections of these chains and emphasize the characterization of roots, which are those points where there is a loss of mass. This is equivalent to studying the incidence graph for the inverse matrix. The main notions and results of this chapter are based on [20] for the ultrametric case and [22] for the GUM case.

Keywords

  • Ultrametric Case
  • Incidence Graph
  • Ultrametric Matrix
  • Dyadic Chaining
  • Matrix Tree

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Fig. 4.1
Fig. 4.2

References

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  2. C. Dellacherie, S. Martínez, J. San Martín, Description of the sub-Markov kernel associated to generalized ultrametric matrices. An algorithmic approach. Linear Algebra Appl. 318, 1–21 (2000)

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© 2014 Springer International Publishing Switzerland

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Dellacherie, C., Martinez, S., San Martin, J. (2014). Graph of Ultrametric Type Matrices. In: Inverse M-Matrices and Ultrametric Matrices. Lecture Notes in Mathematics, vol 2118. Springer, Cham. https://doi.org/10.1007/978-3-319-10298-6_4

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