Python矩阵操作：创建单位矩阵、对角矩阵、零矩阵和全一矩阵

创建单位矩阵、对角矩阵、零矩阵和全一矩阵的示例代码如下：

import numpy as np

# 创建单位矩阵
def create_identity_matrix(n):
    identity_matrix = np.eye(n)
    return identity_matrix

# 创建对角矩阵
def create_diagonal_matrix(values):
    diagonal_matrix = np.diag(values)
    return diagonal_matrix

# 创建零矩阵
def create_zero_matrix(m, n):
    zero_matrix = np.zeros((m, n))
    return zero_matrix

# 创建全一矩阵
def create_ones_matrix(m, n):
    ones_matrix = np.ones((m, n))
    return ones_matrix

# 验证 AXE = EXA = A
def verify_AXE_EXA_A(A, X, E):
    AXE = A.dot(X).dot(E)
    EXA = E.dot(X).dot(A)
    A_result = np.array_equal(AXE, A) and np.array_equal(EXA, A)
    return A_result

# 验证 EXE = E
def verify_EXE_E(E):
    EXE = E.dot(E)
    E_result = np.array_equal(EXE, E)
    return E_result

# 示例用法
A = np.array([[1, 2], [3, 4]])
X = np.array([[2, 0], [0, 2]])
E = create_identity_matrix(2)

identity_matrix = create_identity_matrix(3)
diagonal_matrix = create_diagonal_matrix([1, 2, 3])
zero_matrix = create_zero_matrix(2, 3)
ones_matrix = create_ones_matrix(3, 2)

print('Identity Matrix:')
print(identity_matrix)
print()
print('Diagonal Matrix:')
print(diagonal_matrix)
print()
print('Zero Matrix:')
print(zero_matrix)
print()
print('Ones Matrix:')
print(ones_matrix)
print()

print('Verification of AXE = EXA = A:')
print(verify_AXE_EXA_A(A, X, E))
print()

print('Verification of EXE = E:')
print(verify_EXE_E(E))

运行上述代码，将输出单位矩阵、对角矩阵、零矩阵和全一矩阵的结果，并验证AXE=EXA=A和EXE=E的结果。