On linear-combinatorial problems associated with subspaces spanned by
$\{\pm 1\}$-vectors
On linear-combinatorial problems associated with subspaces spanned by
$\{\pm 1\}$-vectors
A complete answer to the question about subspaces generated by $\{\pm 1\}$-vectors, which arose in the work of I.Kanter and H.Sompolinsky on associative memories, is given. More precisely, let vectors $v_1, \ldots , v_p,$ $p\leq n-1,$ be chosen at random uniformly and independently from $\{\pm 1\}^n \subset {\bf R}^n.$ Then …