import numpy as npdef gram_schmidt(A): # 将A的列向量标准化 Q = A.copy() for i in range(Q.shape[1]): Q[:, i] = Q[:, i] / np.linalg.norm(Q[:, i]) # 计算正交向量 for i in range(1, Q.shape[1]): for j in range(i): Q[:, i] = Q[:, i] - np.dot(Q[:, i], Q[:, j]) * Q[:, j] # 将Q的列向量标准化 Q[:, i] = Q[:, i] / np.linalg.norm(Q[:, i]) return Q想要正交化一个4×1矩阵该如何修改

如果想要正交化一个4×1矩阵，需要对其进行列向量标准化和正交化处理。可以按照以下代码进行修改：

import numpy as np

def gram_schmidt(A):
# 将A的列向量标准化
Q = A.copy()
for i in range(Q.shape[1]):
Q[:, i] = Q[:, i] / np.linalg.norm(Q[:, i])

# 计算正交向量
for i in range(1, Q.shape[1]):
for j in range(i):
Q[:, i] = Q[:, i] - np.dot(Q[:, i], Q[:, j]) * Q[:, j]

# 将Q的列向量标准化
Q[:, i] = Q[:, i] / np.linalg.norm(Q[:, i])

return Q

# 示例
A = np.array([[1], [2], [3], [4]])
Q = gram_schmidt(A)
print(Q) # 打印正交矩阵