- #1
Euge
Gold Member
MHB
POTW Director
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- 243
Here's this week's problem!
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Problem. Let $\nu$ be the differential 2-form $dx_1 \wedge dx_2 + dx_3 \wedge dx_4 + \cdots + dx_{2n-1} \wedge dx_{2n}$ on $\Bbb R^{2n}$. Show that $\nu^n = n!\, dx_1 \wedge dx_2 \wedge dx_3 \wedge \cdots \wedge dx_{2n}$.
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Remember to read the http://www.mathhelpboards.com/showthread.php?772-Problem-of-the-Week-%28POTW%29-Procedure-and-Guidelines to find out how to http://www.mathhelpboards.com/forms.php?do=form&fid=2!
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Problem. Let $\nu$ be the differential 2-form $dx_1 \wedge dx_2 + dx_3 \wedge dx_4 + \cdots + dx_{2n-1} \wedge dx_{2n}$ on $\Bbb R^{2n}$. Show that $\nu^n = n!\, dx_1 \wedge dx_2 \wedge dx_3 \wedge \cdots \wedge dx_{2n}$.
________________
Remember to read the http://www.mathhelpboards.com/showthread.php?772-Problem-of-the-Week-%28POTW%29-Procedure-and-Guidelines to find out how to http://www.mathhelpboards.com/forms.php?do=form&fid=2!