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I Notation (index notation)

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  1. Mar 18, 2016 #1
    I am having trouble converting [D]=[A][ B]T[C] to index notation.
    I initially thought it would be Dij=AijBkjCkl but I have doubts that this is correct.

    Would anyone be able to elaborate on this?

    Regards
     
  2. jcsd
  3. Mar 18, 2016 #2
    Where did B come from?
     
  4. Mar 18, 2016 #3
    BT? It is the transpose of B.
     
  5. Mar 18, 2016 #4
    Err, did you edit your post? I didn't see a B in your equation before. Anyways, nevermind.
     
  6. Mar 18, 2016 #5
    No I never editted the equation. Do you have any ideas?
     
  7. Mar 18, 2016 #6

    Mark44

    Staff: Mentor

    The OP had [B], which browsers treat as the start tag for bold fonts. That screwed up the equation. I edited the equation to fix that problem.
     
  8. Mar 19, 2016 #7

    Svein

    User Avatar
    Science Advisor

    OK. Let us start at the right. First: [itex]B^{T}_{j,k}=B_{k,j} [/itex], so [itex] (B^{T}\circ C)_{j,l}=\sum _{k}B^{T}_{j,k}C_{k,l}[/itex]. Then inset A at the front in the same way: [itex]A\circ (B^{T}\circ C)_{i,l}=\sum _{j}A_{i,j}(\sum _{k}B^{T}_{j,k}C_{k,l}) [/itex].
     
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