quaternions:definitions
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quaternions:definitions [2020/08/05 22:58] – [Identités remarquables et calculs] admin | quaternions:definitions [2020/08/06 18:42] – [Identités remarquables et calculs] admin | ||
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| ::: | $\overline{Q}^{-1}=\frac{Q}{\left|Q\right|^{2}}$ | | | ::: | $\overline{Q}^{-1}=\frac{Q}{\left|Q\right|^{2}}$ | | ||
| ::: | $\left(PQ\right)^{-1}=Q^{-1}P^{-1} $ | | | ::: | $\left(PQ\right)^{-1}=Q^{-1}P^{-1} $ | | ||
- | | exponentiation | + | | exponentiation |
Line 71: | Line 71: | ||
\end{array}\right)$$ | \end{array}\right)$$ | ||
- | est un homomorphisme injectif $\mathbb{H}\to\mathrm{M}(2, | + | est un homomorphisme injectif $\mathbb{H}\to\mathrm{M}(2, |
+ | $$Q \mapsto \left(\begin{array}{cc} | ||
+ | q_{0}+iq_3 & q_1+iq_2\\ | ||
+ | -q_1+iq_2 & q_{0}-iq_3 | ||
+ | \end{array}\right)$$ | ||
- | * l' | + | * l' |
* la conjugaison correspond à la transposition conjugaison des matrices $2 \times 2$ complexes | * la conjugaison correspond à la transposition conjugaison des matrices $2 \times 2$ complexes | ||
+ | |||
+ | |||
==== Forme exponentielle ==== | ==== Forme exponentielle ==== |
quaternions/definitions.txt · Last modified: 2023/11/01 14:44 by 127.0.0.1