Show for tensors (A · B) : C = A^T · C : B = C · B^T : A

  • #1

Homework Statement


using Einstein notation, show the following identities are true

(A · B) : C = A^T · C : B = C · B^T : A



Homework Equations





The Attempt at a Solution


(A · B) : C=(A_{ij} · B_{jk} ) : C
= D_{ik} C_{ik}
= C_{ik} D_{ik}
= C_{ik} (A_{ij} · B_{jk} )

That's as far as I can get. No clue as what to do next, any pointers would be
greatly appreciated :)

Homework Statement





Homework Equations





The Attempt at a Solution

 

Answers and Replies

  • #2
938
9
Bjk = BTkj
 
  • #3
Thanks for the response :)
I got it solved since then, I had trouble trying to convert the double inner product as
a summation. Once I figured that out, it was as easy as pie
 

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