• Support PF! Buy your school textbooks, materials and every day products Here!

Index Notation and Dual Vectors

  • Thread starter BBeltGrl
  • Start date
  • #1
1
0

Homework Statement


Find the dual vector of the following tensor:

6 3 1
4 0 5
1 3 2


Homework 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

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!
 

Answers and Replies

  • #2
Dick
Science Advisor
Homework Helper
26,258
618
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.
 

Related Threads on Index Notation and Dual Vectors

  • Last Post
Replies
11
Views
2K
  • Last Post
Replies
14
Views
4K
  • Last Post
Replies
1
Views
3K
Replies
1
Views
601
  • Last Post
Replies
14
Views
5K
Replies
4
Views
1K
Replies
5
Views
7K
  • Last Post
Replies
2
Views
1K
  • Last Post
Replies
2
Views
767
  • Last Post
Replies
9
Views
1K
Top