I was wondering how to prove the following theorem: (especially the 'if and only if' proof part.) Suppose V is a finite dimensional vector space.

Hi! I was wondering how to prove the following theorem: (especially the 'if and only if' proof part..)

Suppose V is a finite dimensional vector space. Prove that T is diagonalizable if and only if V admits a basis consisting of eigenvectors of T.

Thank you!!