Let V=L2[-1,1] be the Hilbert space of functions over the time interval [-1,1] with inner
Let P 5 V be the subspace of polynomials of order 4 or less, endowed with the inner
product and norm of V, and let
be its natural basis. Define a
linear transformation S as
Show that the subspace P 5 is invariant under S. That is, verify that S maps members of P 5
back into P 5 . Define T as the restriction of S to P 5 .
Hilbert Space, Inner Product and Maps are investigated.