Let V {\displaystyle {}V} be the vector space of the polynomials of degree ≤ d {\displaystyle {}\leq d} . Determine the transformation matrices between the bases u = X 0 , X 1 , X 2 , … , X d {\displaystyle {}{\mathfrak {u}}=X^{0},X^{1},X^{2},\ldots ,X^{d}} and v = P 0 , P 1 , P 2 , … , P d {\displaystyle {}{\mathfrak {v}}=P_{0},P_{1},P_{2},\ldots ,P_{d}} with P 0 = 1 {\displaystyle {}P_{0}=1} and
for d = 0 , 1 , 2 , 3 , 4 {\displaystyle {}d=0,1,2,3,4} .
be the vector space of the
polynomials
of
degree
. Determine the
transformation matrices
between the bases
and
with
and
.
