Transforming T(p(x))= x*p(x)
This shows how multiplication by 
can be performed in a polynomial vector space.
% Define transformation matrix T = [0 0; 1 0; 0 1] % Define a polynomial p(x) = a + bx. In B = {1,x}, it's [a;b] syms a b p = [a;b] % Transform T*p % Which is 0 + ax + bx^2
T =
0 0
1 0
0 1
p =
a
b
ans =
0
a
b