2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/137263The standard theorem for regular stochastic matrices is generalized to matrices with no sign restriction on the entries. The condition that column sums be equal to 1 is kept, but the regularity condition is replaced by a condition on the $\ell_1$-distances between columns.Rings and Algebras15A51text