Изменения
Нет описания правки
|proof =
<tex>\det (\mathcal{A} \cdot \mathcal{B}) {e_1} \land {e_2} \land... \land{e_n} = </tex><br><tex>
(\mathcal{A} \cdot \mathcal{B})^{\wedge_n}{e_1} \land {e_2} \land... \land{e_n} = ^\stackrel{\mathrm{(*)}}{=}</tex><br><tex>(\mathcal{A} \cdot \mathcal{B}) {e_1} \land (\mathcal{A} \cdot \mathcal{B}) {e_2} \land ... \land (\mathcal{A} \cdot \mathcal{B}) {e_n} = ^\stackrel{\mathrm{(def\mathcal{A} \cdot \mathcal{B})}}{=}</tex><br><tex>\mathcal{A} (\mathcal{B} {e_1}) \land \mathcal{A} (\mathcal{B} {e_2}) \land ... \land \mathcal{A} (\mathcal{B} {e_n}) = ^\stackrel{\mathrm{(**)}}{=}</tex><br><tex>\mathcal{A}^{\wedge_n}(\mathcal{B} {e_1} \land \mathcal{B} {e_2} \land ... \land \mathcal{B} {e_n})= ^\stackrel{\mathrm{(***)}}{=}</tex><br><tex>\det \mathcal{A} \cdot (\mathcal{B} {e_1} \land \mathcal{B} {e_2} \land ... \land \mathcal{B} {e_n}) = ^\stackrel{\mathrm{(***)}}{=}</tex><br><tex>
\det \mathcal{A} \cdot \mathcal{B}^{\wedge_n}({e_1} \land {e_2} \land ... \land {e_n}) = </tex><br><tex>
\det \mathcal{A} \cdot \det \mathcal{B} \cdot {e_1} \land {e_2} \land ... \land {e_n} </tex><br>
