Lower bounds on zero-one matrices. (Q1415303)

Let \(R\) , \(U\) denote two zero-one matrices whose product \(T = R \times U\) is the full upper triangular zero-one matrix, i.e. each element is \(1\) if it is not under the main diagonal. By means of elementary tools of linear algebra the author establishes a lower bound for the sum of all entries of both \(R\) and \(U\) and proves that this lower bound is really reached.