Let T be a linear transformation, which acts on a vector space V, over a field F.
Let W be a sub-space which invariants of T, and f,g polynomials from the same field F.
I need to prove that W is invariant of g(T) and f(T)(W) invariant of g(T).
obviously, g(T) is also a linear mapping and therefore is also invariants of W as T does, I just don't know how to prove it correctly.
Have a good day.