can anyone give me a hint on proving this, dx^dy=dxdy dy^dx=-dxdy any words will be appreciated.
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Originally Posted by enricfemi can anyone give me a hint on proving this, dx^dy=dxdy dy^dx=-dxdy any words will be appreciated. A little more context would be helpful P.S. Doesn't the second follow from the first since in any exterior algebra $\displaystyle u\wedge v=-(v\wedge u)$?
Thank you for reply. I rise this question while learning integration on manifolds, especially Stokes's theorem. Does the dx^dy give the orientation of dxdy? then what about dy^dx^dz=-dxdydz? why does the volume can have orientation? Originally Posted by Drexel28 A little more context would be helpful P.S. Doesn't the second follow from the first since in any exterior algebra $\displaystyle u\wedge v=-(v\wedge u)$?
forget anything like dxdy, just treat it as a short form of dx ^ dy.
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