2018年2月21日水曜日

学習環境

数学読本〈6〉線形写像・1次変換/数論へのプレリュード/集合論へのプレリュード/εとδ/落ち穂拾い など(松坂 和夫(著)、岩波書店)の第22章(図形の変換の方法 - 線形写像・1次変換)、22.3(1次変換による色々な図形の像)、固有値と固有ベクトル、問25-(2).を取り組んでみる。



    1. det ( x - 1 1 - 2 x - 3 ) = x 2 - 4 x + 5
      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()

入出力結果(Terminal, Jupyter(IPython))

$ ./sample25.py
(x - 3)⋅(x - 1) + 2

[2 - ⅈ, 2 + ⅈ]

$

1 コメント :

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