Abstract
This monograph deals with well established concepts in linear algebra and Markov chains: M-matrices, their inverses and discrete potential theory. A main focus of this monograph is the so called inverse M-matrix problem, which is the characterization of nonnegative matrices whose inverses are M-matrices. We present an answer given in terms of discrete potential theory. The primary drawback of this representation is the lack of an efficient algorithm for its implementation. The obstacles to securing a simple description have trigged research in subclasses of inverse M-matrices that are described easily. See Johnson and Smith [40] and references therein for more information about this problem.
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Dellacherie, C., Martinez, S., San Martin, J. (2014). Introduction. 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_1
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DOI: https://doi.org/10.1007/978-3-319-10298-6_1
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