Differences

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--- quaternions:definitionsb [2020/08/06 22:36] – [Formules de structure] admin
+++ quaternions:definitionsb [2023/11/01 14:44] (current) – external edit 127.0.0.1
@@ Line 30: / Line 30: @@
 ^ ID ^ Condition ^ Structure ^
-|(S1)| $Z \in \mathbb{B}$ | $\forall \vec{u}\in \vec{\hat{\mathbb{H}}} \ \exists Q_1, Q_2 \in \mathbb{H} : Z=Q_{1}\sigma+Q_{2}\overline{\sigma}$ <html><br></html> avec  $\sigma_{\vec{u}}=\frac{1}{2}(1+i\vec{u})$ |
+|(S1)| $Z \in \mathbb{B}$ | $\forall \vec{u}\in \vec{\hat{\mathbb{H}}} \ \exists Q_1, Q_2 \in \mathbb{H} : Z=Q_{1}\sigma+Q_{2}\overline{\sigma}$ <html><br></html> avec  $\sigma=\frac{1}{2}(1+i\vec{u})$ |
-|(S2)| $Z \in \mathbb{B} - \{0\}$ et $|Z| = 0$  | $\exists q \in \mathbb{H}, \vec{u} \in \vec{\hat{\mathbb{H}}} : Z = q\sigma$ <html><br></html>où $\sigma_{\vec{u}}=\frac{1}{2}(1+i\vec{u})$  |
+|(S2)| $Z \in \mathbb{B} - \{0\}$ et $|Z| = 0$  | $\exists q \in \mathbb{H}, \vec{u} \in \vec{\hat{\mathbb{H}}} : Z = q\sigma$ <html><br></html>avec$\sigma_{\vec{u}}=\frac{1}{2}(1+i\vec{u})$  |
 $\vec{\hat{\mathbb{H}}}$ désigne l'ensemble des quaternions unitaires ($|Q|=1$) purement vectoriels ($\mathbb{S}(Q)=0$)