Transpose Property (where's my mistake)

  • #1
member 428835
Hi PF!

When proving ##\left(AB\right)^T = B^T A^T## I was thinking of writing ##\left(AB\right)_{ij} = A_{ik} B_{kj} = D_{ij}##. Then ##\left(D\right)^T_{ij} = D_{ji} = A_{jk} B_{ki} = A^TB^T## but clearly this is incorrect. Can someone tell me where my mistake is made?

Thanks!
 
Physics news on Phys.org
  • #2
joshmccraney said:
##\left(D\right)^T_{ij} = D_{ji} = A_{jk} B_{ki} = A^TB^T## but clearly this is incorrect.
Yes, the last equality is incorrect.
Hint: ##A_{jk}B_{ki} = (A^T)_{kj}(B^T)_{ik}##.
 
  • #3
joshmccraney said:
Hi PF!

When proving ##\left(AB\right)^T = B^T A^T## I was thinking of writing ##\left(AB\right)_{ij} = A_{ik} B_{kj} = D_{ij}##. Then ##\left(D\right)^T_{ij} = D_{ji} = A_{jk} B_{ki} = A^TB^T## but clearly this is incorrect. Can someone tell me where my mistake is made?

Thanks!

You are using Einstein notation, right?
 
  • #4
micromass said:
You are using Einstein notation, right?
I am, and I think I found the mistake. ##A## initially had a different index, so changing that doesn't make sense, correct?
 

Similar threads

Replies
0
Views
1K
Replies
9
Views
1K
Replies
10
Views
1K
Replies
3
Views
1K
Replies
4
Views
1K
Replies
11
Views
2K
Back
Top