Let us denote a b = max(a; b) and a b = a + b for a; b R and extend this pair of operations to matrices and vectors in the same way as in conventional linear algebra, that is if A = (aij), B = (bij), C = (cij) are real matrices or vectors of compatible sizes then C = A B if cij = k aik bkj for all i; j. If A is a real n