## 2018年2月21日水曜日

### 数学 - Python - 図形の変換の方法 - 線形写像・1次変換 – 1次変換による色々な図形の像 - 固有値と固有ベクトル(固有多項式、実数解、存在の有無)

1. $\begin{array}{}\mathrm{det}\left(\begin{array}{cc}x-1& 1\\ -2& x-3\end{array}\right)\end{array}={x}^{2}-4x+5$
$\frac{D}{4}=4-5=-1<0$

固有多項式は実数解をもたないので、固有値、固有ベクトルなし。

コード(Emacs)

Python 3

#!/usr/bin/env python3
from sympy import pprint, symbols, Matrix, solve

x = symbols('x')
A = Matrix([[1, -1],
[2, 3]])
E = Matrix([[1, 0],
[0, 1]])
eq = (x * E - A).det()

for t in [eq, solve(eq)]:
pprint(t)
print()


$./sample25.py (x - 3)⋅(x - 1) + 2 [2 - ⅈ, 2 + ⅈ]$


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