3.10 矩阵与线性代数运算

问题

需要执行矩阵和线性代数运算，比如矩阵乘法、寻找行列式、求解线性方程组等等。

解决方案

NumPy 库有一个矩阵对象可以用来解决这个问题。

>>> import numpy as np
>>> m = np.matrix([[1,-2,3],[0,4,5],[7,8,-9]])
>>> m
matrix([[ 1, -2, 3],
        [ 0, 4, 5],
        [ 7, 8, -9]])

>>> # Return transpose
>>> m.T
matrix([[ 1, 0, 7],
        [-2, 4, 8],
        [ 3, 5, -9]])

>>> # Return inverse
>>> m.I
matrix([[ 0.33043478, -0.02608696, 0.09565217],
        [-0.15217391, 0.13043478, 0.02173913],
        [ 0.12173913, 0.09565217, -0.0173913 ]])

>>> # Create a vector and multiply
>>> v = np.matrix([[2],[3],[4]])
>>> v
matrix([[2],
        [3],
        [4]])
>>> m * v
matrix([[ 8],
        [32],
        [ 2]])

可以在 numpy.linalg 子包中找到更多的操作函数，比如：

>>> import numpy.linalg

>>> # Determinant
>>> numpy.linalg.det(m)
-229.99999999999983

>>> # Eigenvalues
>>> numpy.linalg.eigvals(m)
array([-13.11474312, 2.75956154, 6.35518158])

>>> # Solve for x in mx = v
>>> x = numpy.linalg.solve(m, v)
>>> x
matrix([[ 0.96521739],
        [ 0.17391304],
        [ 0.46086957]])
>>> m * x
matrix([[ 2.],
        [ 3.],
        [ 4.]])
>>> v
matrix([[2],
        [3],
        [4]])