Question

Please help: Linear Algebra

Answer 1

Let V be the vector space of polynomials over R with inner product defined by \[<f,g>=\int\limits_{1}^{0} f(t)g(t)dt\] let D be the derivative operator on V; that is \[D(f)=df/dt\] show that there is no operator D* on V such that <D(f),g> =<f,D*(g)> for every f, g is an element of V. That is, D has no adjoint.

Answer 2

\[<f,g>=\int\limits_{0}^{1} f(t)g(t)dt\]

Answer 3

Well I'd really appreciate if someone squeezes THAT into this format ......................