Can you guys help me out with solving the following problems.
Here is the problem 1 that I wanted to prove:
Let M: H--> H be diagonalizable (H vector space and W subspace of H). W is M- invariant. Prove that the restriction of M to W is daigonalizable and that T:M/W-->M/W is diagonalizable (note: M/W means M quotient W and not restriction of M to W, i.e the quotient space).
Let M: H--> H has n distinct eigenvalues (note: dimension of H is n).
Let U: H-->H commute with M. show that U is diagonalizable?