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Python 执行矩阵与线性代数运算

问题

你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。
矩阵类似于3.9小节中数组对象,但是遵循线性代数的计算规则。下面的一个例子展示了矩阵的一些基本特性:

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>>>importnumpy 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:

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>>>importnumpy.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]])

>>>

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