Régularité des matrices à diagonale dominante. Applications à l’absorption dans les chaînes et processus de Markov. (Regularity of diagonally dominant matrices. Applications to absorption in Markov chains and processes). (French) Zbl 0584.15008

Lemaire, B.

RAIRO, Rech. Opér. 19, 233-241 (1985).

Theorems concerning the location of the eigenvalues of a matrix in the complex plane allow, in certain circumstances, diagonally dominant matrices to be specified. Such matrices are, however, not always found to arise in the practical problems of applied probability so the author proposes an alternative corollary to deal with such cases.

Reviewer: B.W.Conolly

MSC:

15A42	Inequalities involving eigenvalues and eigenvectors
60J10	Markov chains (discrete-time Markov processes on discrete state spaces)
90B25	Reliability, availability, maintenance, inspection in operations research
62N05	Reliability and life testing

Keywords:

Gerschgorin theorem; Markov chains; Markov processes; reliability; location of the eigenvalues; diagonally dominant matrices