Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Cross Product

  1. May 25, 2007 #1
    Why is it possible to take the cross product in only 3 and 7 dimensions?
     
  2. jcsd
  3. May 25, 2007 #2

    Hurkyl

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    Er, could you clarify the question?


    Although I don't know precisely what you're asking, I suspect the answer has to do with the Quaternions and Octonions.
     
  4. May 25, 2007 #3

    matt grime

    User Avatar
    Science Advisor
    Homework Helper

    If you mean 'why do their exist anti-symmetric linear pairings x/\y : R^nxR^n-->R^n for some n, and not others', then Hurkyl is getting there. There is a theorem in differential geometry that explains this, though I don't know what it is saying (i.e. I can't encapsulate it into a nice bite sized slogan for the lay person).
     
  5. May 25, 2007 #4

    mathwonk

    User Avatar
    Science Advisor
    Homework Helper
    2015 Award

    existence of pairings produces vector fields on the sphere, and these exist only in a few cases. maybe this is related.
     
  6. May 27, 2007 #5
    Well, the idea is that a matrix is created. The determinent can do very funny things. Just try to find the determinents of 3x3, 4x4, 5x5, 6x6, 7x7. You may figure out why...
     
  7. May 27, 2007 #6
    OK. Thanks
     
  8. May 28, 2007 #7

    matt grime

    User Avatar
    Science Advisor
    Homework Helper

    PLease could you elaborate on why determinants of matrices can explain the (non-) existence of smooth (no-where zero, I imagine) vector fields on S^n?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Cross Product
  1. Cross Products (Replies: 8)

  2. Cross product (Replies: 3)

  3. The Cross Product (Replies: 4)

Loading...