1. The problem statement, all variables and given/known data Let V be a finite dimensional complex vector space and T be the linear operator of V. Prove that the following are equivalent a V has a basis consisting of eigenvectors of T. b T can be represented by a diagonal matrix. c all the eigenvalues of T have multiplicity one. d. the Characteristic polynomial of T equals the minimal polynomial of T. 2. Relevant equations Not really applicable 3. The attempt at a solution Ok so I proved A implies B, However, I feel that B does not imply C. I just want to see if my argument is valid. because the identity matrix, is definitely diaganol however, it does not have a multiplicity of One. Can I assume wlog that T has distinct eigenvalues along the main diaganol?