Hankel matrices commuting with tridiagonal matrices

A real Hankel matrix H is said to be generic if there is a non-scalar tridiagonal matrix T which commutes with H. It is proved that: (a) if the symmetric Toeplitz matrix R obtained from a centro-symmetric matrix H by writing the columns in reverse order admits of a non-scalar tridiagonal matrix which commutes with R, then His generic; (b) any Hankel matrix of rank not higher than 2 is generic. (C) 1997 Elsevier Science Ltd.