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

Help with tensor homework

  • #1
1,444
0
if [itex]\epsilon_{ijk} P_{kj}=0[/itex] how do we show [itex]P_{ij}=P_{ji}[/itex]?
 

Answers and Replies

  • #2
dx
Homework Helper
Gold Member
2,011
18


Expand out the LHS for each i.
 
  • #3
1,444
0


do you mean just substitute in numbers and see what happens because that works - i was just wondering if i could do it without explicitly using numbers (i.e. all of it in index notation).
 
  • #4
dx
Homework Helper
Gold Member
2,011
18


For i = j, clearly Aij = Aji, so you only need to check the cases in which i ≠ j.

For example, setting i = 1 in εijkAkj = 0, you get ε123A32 + ε132A23 = A32 - A23 = 0 ⇒ A32 = A23.

You just need to do the same with i = 2 and i = 3.
 

Related Threads for: Help with tensor homework

  • Last Post
Replies
1
Views
896
  • Last Post
Replies
1
Views
519
Replies
1
Views
597
  • Last Post
Replies
5
Views
758
Replies
6
Views
5K
  • Last Post
Replies
2
Views
1K
  • Last Post
Replies
3
Views
842
Replies
4
Views
783
Top