numpy生成希尔伯特矩阵

1.源码实现

import numpy as np

# 希尔伯特矩阵
def hilb(n):
    H = np.zeros((n, n))
    for i in range(n):
        for j in range(n):
            H[i][j] = 1/(i+j+1)
    return H

# 希尔伯特矩阵的逆矩阵
def invhilb(n):
    H = np.zeros((n, n))
    for i in range(n):
        for j in range(n):
            H[i][j] = 1/(i+j+1)
    return np.linalg.inv(H)

print(hilb(3))
print(invhilb(3))

2.运行及其结果

python3 hilb.py 
[[ 1.          0.5         0.33333333]
 [ 0.5         0.33333333  0.25      ]
 [ 0.33333333  0.25        0.2       ]]
[[   9.  -36.   30.]
 [ -36.  192. -180.]
 [  30. -180.  180.]]