Semigroups defined by generalized Schur functions Original Research Article

We prove that the characterization of the singular matrices A satisfying (1) dHλ(AX) = dHλ(XA) for allX can be reduced to that of matrices satisfying (2) dHλ(AX) = 0 for allX, where dHλ is a Schur function. Some partial results on the characterization of (2) are obtained.