Diagonalization of square matrix if not all eigenvalues are distinct of

1. Sep 7, 2011

Uncle_John

Is it possible to diagonalize such matrix? and how would one do it?

2. Sep 7, 2011

micromass

Yes, it is possible to diagonalize such a matrix. One has to find the eigenspaces and a basis for the eigenspaces. Take all the basisvectors for the eigenspaces, if they span the entire space, then the matrix is diagonalizable.
Taking all the basis eigenvectors as a basis gives you the required diagonal matrix.