Question

Using power method to find third largest eigenvalue

Answer 1

Answer:

For example, if A is a diagonalizable matrix, the Power Method fails if both ±λ are eigenvalues of A with the largest absolute value. In particular, suppose A is a 3 × 3 matrix with eigenvalues λ1 = 2, λ2 = −2, and λ3 = 1 and corresponding eigenvectors v1, v2, and v3.