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.
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References
C. Dellacherie, S. Martínez, J. San Martín, Ultrametric matrices and induced Markov chains. Adv. Appl. Math. 17, 169–183 (1996)
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)
S. Martínez, J. San Martín, X. Zhang, A class of M-matrices whose graphs are trees. Linear Multilinear Algebra 52(5), 303–319 (2004)
R. Nabben, R.S. Varga, Generalized ultrametric matrices – a class of inverse M-matrices. Linear Algebra Appl. 220, 365–390 (1995)
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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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DOI: https://doi.org/10.1007/978-3-319-10298-6_4
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Online ISBN: 978-3-319-10298-6
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