First problem: Assume T: V -> V is a Hermitian transformation
Prove T^-1 is Hermitian if T is invertible.
Here, I can prove that T^n is Hermitian if n > 0 but I'm stuck for n = -1.
Second Problem: C(0, 1) is linear Space. Inner product is given by:
(f, g) = integral( f * g, t, 0, 1).
Let V be the subspace of all f such that integral f, t, 0, 1) = 0.
Let T: V -> C(0, 1) and T(f(x)) = integral(f, t, 0, x). Prove T is skew - symmetric.
For this problem, I would apply the transformation, do the inner product, then I would have an integral in an integral. I don't know if I should F and G for their anti derivative or what.