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Reciprocal basis problem

  1. Aug 26, 2008 #1
    1. The problem statement, all variables and given/known data

    Let {a,b,c} be any basis set. Then the corresponding reciprocal {a*,b*,c*} is defined by
    a*=b x c/[a,b,c] , b*=c x a/[a,b,c], c*=a x b/[a,b,c]

    If {i,j,k} is standard basis, show that {i*,j*,k*}={i,j,k}

    2. Relevant equations

    3. The attempt at a solution

    I have no idea how to start this problem. I know the standard basis is just the identity matrix. But thats all I know. I don't know what {i*,j*,k*} is supposed to symbolized. Is it the inverse of {i,j,k}?
  2. jcsd
  3. Aug 26, 2008 #2
    Did anyone not understand my question?
  4. Aug 26, 2008 #3

    Ben Niehoff

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    Science Advisor
    Gold Member

    What is the notation [a,b,c]? A vector triple product?

    Also, {i,j,k} is not a matrix. It is a set of three vectors.
  5. Aug 26, 2008 #4


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    Staff Emeritus
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    First you are going to have to clarify your notation. Is a x b the cross product of two vectors or is it a tensor product? And what do you mean by [a, b, c]?
  6. Aug 26, 2008 #5

    a x b is the cross product [a,b,c] is the basis set.
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