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 = (ai j),B = (bi j),C = (ci j) are real matrices or vectors of compatible sizes then C = A⊗ B if ci j = ⊕ k aik ⊗ bk j for all i, j. For any n× n matrix A = (ai j) and for arbitrary sequence of real parameters α = (α1, . ...