Stretching and Contraction
Theorem
Let $s_\beta: \R^2 \to \R^2$ be a similarity of $\R^2$.
Then $s_{-1}$ is the same as the rotation $r_{\pi}$ of the plane about the origin one half turn.
If $\beta \ge 1$, then $s_\beta$ is called a stretching, and if $0 < \beta \le 1$, $s_\beta$ is called a contraction.
If $\beta < 0$, then $s_\beta$ is a stretching or contraction followed by a rotation one half turn. It is also the same as a rotation one half turn followed by a stretching or contraction.
Proof
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Sources
- Seth Warner: Modern Algebra (1965): $\S 28$: Example $28.3$
