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Math Help - exterior algebra in R3

  1. #1
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    exterior algebra in R3

    can anyone give me a hint on proving this,

    dx^dy=dxdy
    dy^dx=-dxdy

    any words will be appreciated.
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  2. #2
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by enricfemi View Post
    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 u\wedge v=-(v\wedge u)?
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  3. #3
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    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?


    Quote Originally Posted by Drexel28 View Post
    A little more context would be helpful

    P.S. Doesn't the second follow from the first since in any exterior algebra u\wedge v=-(v\wedge u)?
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  4. #4
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    forget anything like dxdy, just treat it as a short form of dx ^ dy.
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