A is n by n matrix. It is diagonalized by P. Find the matrix that diagonalizes the tranpose of A. We have the equation A=PDP^-1 Where D is the diagonal matrix consisting of the eigen values of A. (A)^t=(PDP^-1)^t A^t=(P^-1)^t * D^t * P^t A^t=(P^t)^-1 * D * P^t So the matrix (P^t)^-1 diagonalizes A^t. Is that correct?