use Similarity Transformation like
Householder transformation
we can use Householder transformation as
def deflate_matrix(A, eigenvector, eigenvalue):
# Normalize the eigenvector
v = eigenvector / np.linalg.norm(eigenvector)
# Householder matrix: H = I - 2vv^T
H = np.eye(A.shape[0]) - 2 * np.outer(v, v)
# Deflated matrix: A' = H A H
# bc H^{-1} = H in this case
A_deflated = H @ A @ H
return A_deflated