Can anyone tell me clearly what the criteria for isomorphism in linear algebra is? For instance, my book gives the following reason: Transformation T is not isomoprhic because T((t-1)(t-3)) = T(t^2 - 4t +3) = zero vector. I don't get why this means T is not an isomorphism. Can anyone explain? PS. T is a transformation from P_2 to R^(3). the actual T is: T(f(t)) = f(1) f'(2) f(3) Thanks.