Pythonで特異値分解してみる ref: http://qiita.com/kyoro1/items/4df11e933e737703d549

file0.txt

A=U\Sigma \overline{V^T}

file1.txt

A=\left(
\begin{matrix}
1 & 2 \\
3 & 4 
\end{matrix}
\right)

file10.py

> np.dot(V, V.T)
array([[ 1.,  0.],
       [ 0.,  1.]])

file2.py

> import numpy as np
> A = np.array([[1,2],[3,4]])

file3.py

> A 
array([[1, 2],
       [3, 4]])

file4.py

U, s, V = np.linalg.svd(A, full_matrices=True)

file5.py

> U
array([[-0.40455358, -0.9145143 ],
       [-0.9145143 ,  0.40455358]])
> s
array([ 5.4649857 ,  0.36596619])
> V
array([[-0.57604844, -0.81741556],
       [ 0.81741556, -0.57604844]])

file6.py

> np.diag(s)
array([[ 5.4649857 ,  0.        ],
       [ 0.        ,  0.36596619]])

file7.txt

A=U\Sigma \overline{V^T}

file8.py

>np.dot(np.dot(U, np.diag(s)),V)
array([[ 1.,  2.],
       [ 3.,  4.]])

file9.py

> np.dot(U, U.T)
array([[  1.00000000e+00,   2.77555756e-16],
       [  2.77555756e-16,   1.00000000e+00]])