Irreducible Toeplitz and Hankel matrices

Abstract

An infinite matrix is called irreducible if its directed graph is strongly connected.
It is proved that an infinite Toeplitz matrix is irreducible if and only if almost every finite leading
submatrix is irreducible. An infinite Hankel matrix may be irreducible even if all its finite leading
submatrices are reducible. Irreducibility results are also obtained in the finite cases.