We show that any bounded matrix of linear functionals [ f i j ] : M n ( A ) → M n ( ℂ ) has a representation f i j ( a ) = 〈 T π ( a ) x j , x i 〉 , a ∈ A , i , j = 1 , 2 , … , n , for some representation π on a Hilbert space K and an n vectors x 1 , x 2 , … , x n in K .