Python 执行矩阵与线性代数运算

> 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]])
>

> 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]])
>