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On semigroups of matrices with nonnegative diagonals (1209.3882v1)
Published 18 Sep 2012 in math.FA
Abstract: We give a short proof of a recent result by Bernik, Mastnak, and Radjavi, stating that an irreducible group of complex matrices with nonnegative diagonal entries is diagonally similar to a group of nonnegative monomial matrices. We also explore the problem when an irreducible matrix semigroup in which each member is diagonally similar to a nonnegative matrix is diagonally similar to a semigroup of nonnegative matrices.