Abstract
In this chapter we investigate the relationship between M-matrices, their inverses and potentials of finite Markov chains. We supply the basic concepts from potential theory and put them in a linear algebra perspective. We highlight the concepts of potential matrices, equilibrium potentials and maximum and domination principles. The primary results are the characterizations of inverse M-matrices given in Theorems 2.15 and 2.29. The former is based on the domination principle while the latter is based on time continuous positive semigroups. We also illustrate the relationship between potential matrices and electrical networks.
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Dellacherie, C., Martinez, S., San Martin, J. (2014). Inverse M-Matrices and Potentials. 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_2
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DOI: https://doi.org/10.1007/978-3-319-10298-6_2
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