Pythonで逆行列を求める＆検算 ref: http://qiita.com/kyoro1/items/9ff500db0d519bd2a6f5

file0.txt

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

file1.py

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

file10.py

> np.dot(A,inv_A)
array([[  1.00000000e+00,   1.11022302e-16],
       [  0.00000000e+00,   1.00000000e+00]])
> np.dot(inv_A,A)
array([[  1.00000000e+00,   4.44089210e-16],
       [  0.00000000e+00,   1.00000000e+00]])

file2.py

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

file3.txt

{\rm det}(A)={\rm det}\left(
\begin{matrix}
1 & 2 \\
3 & 4 
\end{matrix}
\right)
=1\times 4-2\times3=-2

file4.py

> np.linalg.det(A)
-2.0000000000000004

file5.txt

A = \left(
\begin{matrix}
a & b \\
c & d
\end{matrix}\right)

file6.txt

A^{-1} = \frac{1}{{\rm det}A}\left(
\begin{matrix}
d & -b \\
-c & a
\end{matrix}\right)

file7.txt

A^{-1} = \frac{1}{-2}\left(
\begin{matrix}
4 & -2 \\
-3 & 1
\end{matrix}\right)
=\left(
\begin{matrix}
-2 & 1 \\
1.5 & -0.5
\end{matrix}
\right)

file8.py

> inv_A = np.linalg.inv(A)
> inv_A
array([[-2. ,  1. ],
       [ 1.5, -0.5]])

file9.txt

AA^{-1}=A^{-1}A=
\left(
\begin{matrix}
1 & 0 \\
0 & 1
\end{matrix}
\right)