How do I convert [D]=[A][ B]T[C] to index notation?

In summary, the conversation discusses the difficulty of converting [D]=[A][ B]T[C] to index notation. The initial suggestion is Dij=AijBkjCkl, but this is doubted to be correct. There is a request for elaboration and it is revealed that B is the transpose of B. There is confusion about the equation due to formatting issues, but it is eventually resolved by inserting A in the correct place.
  • #1
kezzstar
8
0
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
 
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  • #2
Where did B come from?
 
  • #3
Khashishi said:
Where did B come from?
BT? It is the transpose of B.
 
  • #4
Err, did you edit your post? I didn't see a B in your equation before. Anyways, nevermind.
 
  • #5
Khashishi said:
Err, did you edit your post? I didn't see a B in your equation before. Anyways, nevermind.
No I never editted the equation. Do you have any ideas?
 
  • #6
Khashishi said:
Err, did you edit your post? I didn't see a B in your equation before. Anyways, nevermind.
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.
 
  • #7
kezzstar said:
I am having trouble converting [D]=[A][ B]T[C] to index notation.
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].
 

1. What is notation (index notation)?

Notation (index notation) is a mathematical system used to represent and manipulate quantities and equations using indices or subscripts. It is commonly used in fields such as physics and engineering.

2. How is notation (index notation) different from other mathematical notations?

Notation (index notation) is different from other mathematical notations because it uses indices or subscripts to represent quantities, rather than traditional symbols and operators. This makes it more compact and easier to work with when dealing with complex equations or multiple variables.

3. What are the advantages of using notation (index notation)?

There are several advantages to using notation (index notation). It allows for easier manipulation and simplification of complex equations, improves readability and compactness of equations, and is especially useful for representing vector and tensor quantities.

4. Are there any limitations or drawbacks to using notation (index notation)?

One limitation of notation (index notation) is that it can be difficult to learn and understand at first, especially for those who are not familiar with it. It also may not be suitable for all types of equations, as certain types of calculations may be more easily done using other notations.

5. How can I learn and get better at using notation (index notation)?

The best way to learn and improve at using notation (index notation) is to practice. Familiarize yourself with the basic rules and conventions, and then work on solving equations using this notation. Additionally, seeking guidance and resources from textbooks or online tutorials can also be helpful.

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