Hankel planes

Starting from an (m+1)×(n+1) matrix A one can construct (m+p+1)×(n+1)(p+1) block Toeplitz matrices TAρ(p), p≥0, based on the rows of A. The connections between the ranks of the two matrices is studied by comparing the corresponding vector spaces of row relations R and R(p). A main tool are the Hankel matrices with rows in R. The dimension of R(p) is determined in terms of geometric invariants attached to the Hankel matrices with rows in R. The study of Hankel r-planes of Pm, for r≥1, turns out to be very useful and interesting in itself since they constitute a subvariety of the Grassmannian G(r,m).