Structure of H-classes in the semigroup of nonnegative matrices

AbstractThis paper investigates the structure of the H-classes in the semigroup Nn of nonnegative matrices. We obtain two sets of equivalent conditions for any two matrices A,B to satisfy AHB in Nn. We establish a one-to-one and onto correspondence between the H-class HA and the group WA0 of the greatest cone independent submatrix A0 of A. We find WA0 can be made up from the groups of the connective submatrices of A0