Abstract

We study non-singular ultrametric matrices A. These kinds of matrices are restrictions of non-singular tree matrices. The structure of A-1 allows us to associate to A some substochastic kernels P. We are able to describe the graph of P, in particular those vertices which lose mass. Our main tools are an algebraic decomposition lemma of A-1 and the study of the minimal tree matrix associated to A. © 1996 Academic Press, Inc.