Problem 2. Let F = C and V be the vector space {ao + a1x + ... + anx" : 01, ..., An E C} be the vector space of degree n
Posted: Tue Sep 07, 2021 7:44 am
Problem 2. Let F = C and V be the vector space {ao + a1x + ... + anx" : 01, ..., An E C} be the vector space of degree n polynomials. Let T: V + V be given by T(f) = f'. Show that T is not diagonalizable. (I have heard professional mathematicians say that every matrix over C is diagonalizable! This is not true.)