Let P_n be the real vector space of all polynomials of degree at most n. Let D : P_n → P_n-1, and T : P_n → P_n+1 be the linear transformations defined by

D(a₀ + a₁x + a₂x² + .....+a_nxⁿ) = a₁ + 2a₂x + .... + na_nx^n-1

T(a0 + a1x + a2x2 + .....+anxn) = a₀x + a₁x² + ..... + a_nxⁿ⁺¹

respectively. If A is the matrix representation of the transformation DT - TD : P_n → P_n with respect to the standard basis of P_n then the trace of A is