Structure of \({\mathcal H}\)-classes in the semigroup of nonnegative matrices
This paper inestigates the structure of the \({\mathcal H}\)-classes in the semigroup \(N_ n\) of nonnegative matrices: The main results are as follows. (1). Two sets of equivalent conditions for any two matrices A and B to satisfy A\({\mathcal H}B\) in \(N_ n\) are obtained. (2) A one-to-one and onto correspondence between the \({\mathcal H}\)-class \({\mathcal H}_ A\) and the group \(W_{A_ 0}\) of the greatest cone-independent submatrix \(A_ 0\) of A is established. (3) \(W_{A_ 0}\) can be made up from the groups of the connective submatrices of \(A_ 0\).
scientific article; zbMATH DE number 3861343