On the inverse mean first passage matrix problem and the inverse M-matrix problem

Michael Neumann, Nung Sing Sze

Research output: Journal article publicationJournal articleAcademic researchpeer-review

9 Citations (Scopus)


The inverse mean first passage time problem is given a positive matrix M∈Rn,n, then when does there exist an n-state discrete-time homogeneous ergodic Markov chain C, whose mean first passage matrix is M? The inverse M-matrix problem is given a nonnegative matrix A, then when is A an inverse of an M-matrix. The main thrust of this paper is to show that the existence of a solution to one of the problems can be characterized by the existence of a solution to the other. In so doing we extend earlier results of Tetali and Fiedler.
Original languageEnglish
Pages (from-to)1620-1630
Number of pages11
JournalLinear Algebra and Its Applications
Issue number7
Publication statusPublished - 1 Apr 2011


  • Diagonally dominant M-matrices
  • Inverse M-matrices
  • Markov chains
  • Mean first passage times
  • Nonnegative matrices
  • Stationary distribution

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Numerical Analysis
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics

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