Question

Let V = R1[x], consider the map T : V −→ V given by T(p) =...

Let V = R1[x], consider the map T : V −→ V given by T(p) = p(1)+p(−1)x. Suppose V has the inner product given by〈p, q〉 = p(1)q(1) + p′(1)q′(1)

What is T∗(x)? Show how to get the answer 7-4x

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Answer #1


with inner product

Then the adjoint is found by solving

Substituting we get

Equation becomes

So that

Therefore,

Now we substitute and

So means

Therefore,

Thus,

Noting that and so that

And we get the solution as as required

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