A Vandermonde Matrix is a square matrix (having size nxn), if and only if there are scalars, x₁, x₂ , x₃,…, x_n  such that,

当且仅当存在标量x ₁ ，x ₂ ，x ₃ ，…，x _n时 ，Vandermonde矩阵是方矩阵(大小为n x n )，

Source: https://en.wikipedia.org/wiki/Vandermonde_matrix

资料来源： https : //en.wikipedia.org/wiki/Vandermonde_matrix

Python numpy package allows us to create a Vandermonde Matrix by providing an inbuilt function numpy.vander().

Python numpy包允许我们通过提供内置函数numpy.vander()创建Vandermonde矩阵。

Vandermonde矩阵的Python代码 (Python code for vandermonde matrix)

# Linear Algebra Learning Sequence
# Vandermonde Matrix
import numpy as np
x = np.array([1, 2, 3, 5])
N = 3
v1 = np.vander(x)
print('Vector x :\n', x)
print('Vandermonde Matrix of vector x', v1)
y = np.array([4,5,6,7,8,9])
N = 4
v2 = np.vander(y, N)
v3 = np.vander(y)
print('\n\nVector y :\n', y)
print('Vandermonde Matrix of vector y (N = 4): ', v2)
print('\n\n Vandermonde Matrix (Square) of vector y : ', v3)

Output:

输出：

Vector x :
[1 2 3 5]
Vandermonde Matrix of vector x [[  1   1   1   1]
[  8   4   2   1]
[ 27   9   3   1]
[125  25   5   1]]
Vector y :
[4 5 6 7 8 9]
Vandermonde Matrix of vector y (N = 4):  [[ 64  16   4   1]
[125  25   5   1]
[216  36   6   1]
[343  49   7   1]
[512  64   8   1]
[729  81   9   1]]
Vandermonde Matrix (Square) of vector y :  [[ 1024   256    64    16     4     1]
[ 3125   625   125    25     5     1]
[ 7776  1296   216    36     6     1]
[16807  2401   343    49     7     1]
[32768  4096   512    64     8     1]
[59049  6561   729    81     9     1]]

翻译自: https://www.includehelp.com/python/vandermonde-matrix.aspx