  Let A be a k-vector space of dimension a. A subvector space M of End(A) is
said to be of rank r if every non-zero f in M has rank r. The problem
considered in this paper is to determine l(r;a) the maximal dimension of a rank
r subspace of End(A). Known results are reviewed in the language of vector
bundles. Some new results are proved and a conjecture is made.
