ON MINIMAL SETS OF -MATRICES WHOSE PAIRWISE PRODUCTS FORM A BASIS FOR

Abstract

Three families of examples are given of sets of $(0,1)$-matrices whose pairwise products form a basis for the underlying full matrix algebra. In the first two families, the elements have rank at most two and some of the products can have multiple entries. In the third example, the matrices have equal rank $\!\sqrt{n}$ and all of the pairwise products are single-entried $(0,1)$-matrices.