Using the power method on a matrix that has been deflated twice

Question

So, according to what I've learned these 4 are true:

1. The power method requires a diagonalizable matrix A
2. A requirement for a matrix to be diagonalizable is that all of its eigenvalues are distinct
3. Deflating a matrix A using eigenvalue lambda (and corresponding eigenvector) will result in a new matrix B with the same eigenvalues as A, except lambda is replaced with 0 (and with new eigenvectors).
4. All eigenvalues of A can be found by repeating the power method + deflation

These seem contradictory. If I deflate A twice, two of its eigenvalues will be 0, no? Then it won't have distinct eigenvalues, meaning it's not diagonalizable, meaning I can't use the power method to find the next eigenvalue. How is it possible to find the third eigenvalue in this case?

Answer 1

Having distinct eigenvalues is a sufficient condition for a matrix to be diagonalizable, but not a necessary one. For example, any diagonal matrix is diagonalizable.