1. The problem statement, all variables and given/known data I have a transformation (not linear! that is what I have to show) F given by: F : P_4 -> P_7 (P_7 is the vector-space spanned by polynomials less than degree 7). I also know that F(p(x)) = (p(x))^2. The matrix A representing F with respect to the two basis is the one I get by taking the transformation F on P_4's elements [x^3, x^2, x, 1] and expressing by P_7's elements. I get a 7x4-matrix with 4 zeroes and the rest are zero-entries. 3. The attempt at a solution This matrix is the matrix A in L(x) = Ax. So if I take a polynomial in P_4 and multiply with A, it should be squared: A*(a_1*x^3, a_2*x^2, a_3*x, a_0)^T. But this doesn't make a_1*x^3 go to (a_1)^2*x^6 and so on? Where am I going wrong? I hope you understand my questions. Sincerely, Niles.