Find the eigenvalues of the matrix by solving the characteristic equation det(A – λI) = 0
Find a basis for each eigenspace by solving (A – λI)x = 0 for each eigenvalue
Check that the matrix has enough linearly independent eigenvectors to form a basis
Form the matrix P using the eigenvectors as columns
Form the diagonal matrix D using the corresponding eigenvalues in the same column order
Verify that A = PDP^-1
If there are not enough linearly independent eigenvectors, the matrix is not diagonalizable