The group inverse of the transformation J(X) = AX − XB Original Research Article

The group inverse image# of the Sylvester transformation J(X) = AX − XB is (provided that it exists) represented in polynomial form J#(Y) = ΣijcijAiYBj in terms of the minimal polynomials of A and B. In one of the representations the coefficient matrix [cij] is expressed with the help of a new class of “derived” Hankel matrices.