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Derivate of geometrical product

  1. Apr 15, 2005 #1
    Dear Friends

    I'd like to know if anybody has the solution of the aplication of nabla's operator to geometrical product:

    ab=a·b+a^b

    And if it's possible to apply a operator like this:

    d/dt + d/dx i + d/dy j + d/dz k.

    My best reggards.
     
  2. jcsd
  3. Apr 15, 2005 #2

    quasar987

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    What is the geometrical product? Mathworld doesn't know.

    About "d/dt + d/dx i + d/dy j + d/dz k". You wish to apply this operator to a scalar function? I don't know but the result would be a scalar + a vector. The operation of addition is not defined between those two identities afaik.
     
  4. Apr 15, 2005 #3

    Hurkyl

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    It sounds a lot like the OP is working with quaternions... as a real vector space, their standard basis vectors are often written 1, i, j, k. The 1 is often suppressed. :smile:

    It's also true that [itex]a b = a\cdot b \vec{1} + a \times b[/itex], where the first product is ordinary quaternion multiplication.
     
  5. Apr 16, 2005 #4

    robphy

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  6. Apr 17, 2005 #5
    Thanks!!! very useful!
     
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