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Question Number 145411 by puissant last updated on 04/Jul/21

$$\mathrm{un}\mathrm{espace}\mathrm{vectoriel}{\mathrm{n}}^{\prime }\mathrm{as}\mathrm{un}\mathrm{seul}$$$$\mathrm{hyper}-\mathrm{plan}..\mathrm{quelle}\mathrm{est}\mathrm{sa}\mathrm{dimension}.?$$

Answered by Olaf_Thorendsen last updated on 04/Jul/21

$${\mathrm{L}}^{\prime }\mathrm{une}\mathrm{des}\mathrm{definitions}\mathrm{des}\mathrm{hyperplans}$$$$\mathrm{entraine}\dim \left(\mathrm{H}\right)=\dim \left(\mathrm{E}\right)-1=n-1$$$$$$$$\mathrm{Sauf}\mathrm{erreur},\mathrm{la}\mathrm{seule}\mathrm{facon}\mathrm{de}\mathrm{ne}\mathrm{pas}$$$$\mathrm{avoir}{\mathrm{d}}^{\prime }\mathrm{hyperplans}\mathrm{est}:$$$$\dim \left(\mathrm{H}\right)=0$$$$\Rightarrow n=1$$$$\mathrm{E}\mathrm{est}\mathrm{alors}\mathrm{une}\mathrm{droite}\mathrm{vectorielle}$$

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