An alternative simple proof for a well-known result encountered in blind id
entification and equalization of communication channels is derived, It is s
hown that the coprimeness condition of a number of FIR channels is equivale
nt to the full column rank condition of a certain block Sylvester matrix, w
hose entries are the channel coefficients. As a corollary, it is also shown
that in general, the null space of a block Sylvester matrix is spanned by
the set of (generalized) Vandermonde vectors associated with the common zer
os present in all the channels.