Hello,
i would like help with this:
Assume that T : V ....> V is linear and that n and k are positive integers and that a_0,a_1,a_2,.....,a_n are scalars. Let U = a_0IV + a_1T + a_2T^2 + + a_nT^n. Show that T^kU = UT^k.
Use from 1 to 6:
(1) Since
L(V, V ) is a vector space all of the vector space properties hold for addition and scalar multiplication.
(2) T(U1U2) = (TU1)U2.
(3) ) T(U1 + U2) = (TU1) + (TU2).
(4) (U1 + U2)T = U1T + U2T.
(5) For any non-negative integers i and j, T^iT^j = T^i+j .
(6) For any scalars c and d, (cT )(dU1) = (cd)TU1.
Thank you