BBeltGrl
Feb21-08, 03:25 PM
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!
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!