Abstract: We study vector spaces W of quadratic forms in 2, 3 and 4 variables. The main results give the possible numbers of rank 1 and 2 forms in the projective space defined by W, with particular attention given to the case where the dimension of W is equal to the number of variables. We outline the connection of this problem with the representation theory of regular Clifford algebras.
This paper has been submitted for publication. Download a preprint in PDF format (154KB): PDF (February 9, 2007)