我正在尝试使用 QR 方法找到矩阵 A 的特征向量。我找到了对应于最大特征值的特征值和特征向量。如何在不使用 numpy.linalg.eig 的情况下找到其余的特征向量？

import numpy as np

A = np.array([
    [1,0.3],[0.45,1.2]
])

def eig_evec_decomp(A,max_iter=100):
    A_k = A
    Q_k = np.eye(A.shape[1])
    
    for k in range(max_iter):
        Q,R = np.linalg.qr(A_k)
        Q_k = Q_k.dot(Q)
        A_k = R.dot(Q)

    eigenvalues = np.diag(A_k)
    eigenvectors = Q_k
    
    return eigenvalues,eigenvectors
 
evals,evecs = eig_evec_decomp(A)
print(evals)
# array([1.48078866,0.71921134])

print(evecs)
# array([[ 0.52937334,-0.84838898],#       [ 0.84838898,0.52937334]])

接下来我检查条件：

Ax=wx  
Where:
A - Original matrix;  
x - eigenvector;  
w - eigenvalue. 

检查条件：

print(np.allclose(A.dot(evecs[:,0]),evals[0] * evecs[:,0]))
# True
print(np.allclose(A.dot(evecs[:,1]),evals[1] * evecs[:,1]))
# False