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Index Notation and Dual Vectors

  1. Feb 21, 2008 #1
    1. The problem statement, all variables and given/known data
    Find the dual vector of the following tensor:

    6 3 1
    4 0 5
    1 3 2

    2. Relevant equations

    dj= EijkTik

    Where Eijk = 1 if ijk=123, 231, 312
    Eijk = 0 if i=j i=k or j=k
    Eijk = -1 if ijk = 132, 213, 321

    3. The attempt at a solution

    Ok, so I'm not really sure how to solve this but my thought is that it is simply multiply diagonally across the matrix such that

    dj= (6*0*2)*(1) + (3*5*1)(1) +(1*4*3)*(1) + (1*0*1)(-1) + (6*5*3)(-1) +(3*4*2)(-1)

    However, I don't see how that gets me a vector in the end.

    Please HELP!
  2. jcsd
  3. Feb 21, 2008 #2


    User Avatar
    Science Advisor
    Homework Helper

    dj is the jth component of the dual vector. So there are three different values d1, d2 and d3. Just put j=1,2,3 and find them.
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