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