1. The problem statement, all variables and given/known data A = 000 010 101 Find Eigenvalues, its corresponding eigenvectors, and find a matrix W such that W^t*AW = D, where D is a diagnol matrix.(note that W^t represents the transpose of W) 2. Relevant equations Eigenvalues, Eigenvectors, diagnolization 3. The attempt at a solution Question 1 is to find eigenvalues. Since it is already a lower triangular matrix this was easy and I believe the eigenvalues are 1 and 0. The characteristic equation I got was (0-y)(1-y)(1-y). Question 2 was to find the corresponding eigenvectors. if y1 = 1, then (A-1I) = -100 000 100 From that you get x1 = 0. x2 and x3 are free. So a basis for the eigenspace is (v1, v2) where v1 = 0 1 0 v2 = 0 0 1 For y = 0, A -0 is just A. you get x2 = 0 and x1 = -x3 with x3 free. Therefore the corresponding eigenvector is v = -1 0 1 Correct me if I'm wrong but I believe up to here I have done everything correct. The final part of the question confuses me quite a bit . "find a matrix W such that W^t*AW = D, where D is a diagnol matrix." I thought diagnolization is only possible if a matrix is invertible. Since A has 0 as an eigenvalue, it is not invertible. Did I get the eigenvectors wrong or is D not the diagnolization of A? Edit: I cannot find a way to get the space formatting correct. Does anyone know how?