Reciprocal basis problem

  • Thread starter Benzoate
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Homework Statement



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}

Homework Equations





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}?
 

Answers and Replies

  • #2
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Did anyone not understand my question?
 
  • #3
Ben Niehoff
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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.
 
  • #4
HallsofIvy
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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]?
 
  • #5
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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]?



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

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