Positive commutators and collections of operators
Positive commutators and collections of operators
Let A and B be completely decomposable nonnegative matrices such that the commutator AB -BA is also a nonnegative matrix.We prove that the set {A,B} is completely decomposable, i.e., there exists a permutation matrix P such that PAP -1 and PBP -1 are upper triangular matrices.We show similar results for …