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Mathematik-Online problems:

Problem 88: Map of a Square onto itself

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
The shown square $ Q\subset\mathbb{R}^2$ has the vertices $ P_1=(-1, -1)$, $ P_2=(1, -1)$, $ P_3=(1, 1)$ und $ P_4=(-1, 1)$.

\includegraphics[width=2.5cm]{g35_bild1}
a)
Find all linear maps $ \alpha: \mathbb{R}^2\longrightarrow\mathbb{R}^2$ which fix $ Q$.
b)
Show that the maps form a group with respect to the composition $ \circ$.

(Authors: Kimmerle/Höfert)

see also:

[Solutions]
  automatisch erstellt am 14. 10. 2004