diagonalizable? If A DOES NOT have distinct eigenvalues, eg 2 eigenvalue not distinct but D=digonal(all eigenvlues of A) is linearly independent => det(D)=/= 0 in addition CD = AC Is A diagonalizable? Solution is not necessarily equal to A. For different nonsingular matrices P, the above expression will ... If A and B are similar matrices, then they have the same eigenvalues. ... A matrix A is diagonalizable if A is similar to a diagonal matrix D. ... Since the l\'s are distinct, the ci\'s must all be zero, which is a contradiction.