SOLVED:Prove that the restriction of a diagonalizable linear operator T to any nontrivial T-invariant subspace is also diagonalizable. Hint: Use the result of Exercise 23

[GET ANSWER] Let T be a linear operator on a finite-dimensional vector space V over a field 𝔽 such that all the roots of the characteristic polynomial of T are in 𝔽. Prove that T is diagonalizable if and only if for every eigenvalue a of T Ker(T-a I)=Ker(T-a I)^kfor every integer k ≥ 2, where I is the identity operator on V.