Matrix multiplication: index / suffix notation issues

In summary, the conversation revolves around the use of summation notation for matrix and vector operations, particularly multiplication. The first summation is deemed correct, while the notation for the next one is incorrect. The correct formula for (ABC) is given, and it is clarified that the order in which terms are added does not matter. The correct way to multiply four matrices (A, B, C, and D) is also provided, with a reminder to use proper brackets. The use of (AB)C_ij is noted as confusing and the correct notation of (ABC)_ij is emphasized. The conversation ends with the person seeking help thanking the expert and mentioning the possibility of asking more questions in a new thread.
  • #1
Dixanadu
254
2
Hey everyone,

I'm struggling with the summation notation for matrices and vector operations, multiplication in particular. Please refer to the image below where I've typed it all out in Word, its too cumbersome here and I want my meaning to be clear:
https://imageshack.us/scaled/large/580/indicesquestion1.jpg [Broken]
 
Last edited by a moderator:
Mathematics news on Phys.org
  • #2
Ah man that image turned out tiny...If you guys need it to be bigger please let me know!
 
  • #3
Your first summation for ##(AB)_{ij}## is ok.

Your notation for the next one isn't right. If you want to multiply (AB) by C, you have
$$(ABC)_{ij} = \sum_l^L (AB){}_{il}C_{lj}$$

Now plug in the summation for ##(AB)_{il}## and you get
$$(ABC)_{ij} = \sum_l^L (\sum_k^K A_{ik}B_{kl})C_{lj}$$

You got to the right formula in the end, but (as you said) not in a very logical way.
 
  • #4
Okay, thank you, I still have a few more questions but for the time being, can you tell me if I can swap the sigma symbols without reordering the suffixes?
 
  • #5
It doesn't matter what order you add up the terms. Changing the order is the same as saying a+b+c+d+e+f = a+d+b+e+c+f, or whatever order you like.
 
  • #6
Alright. Just to make sure that I understand this properly...let's say I want to multiply 4 matrices A B C D together, where the multiplication is possible. Does it go like this:

https://imageshack.us/scaled/large/853/summationquestion.jpg [Broken]

Hopefully its right T_T and now the image is too big :(
 
Last edited by a moderator:
  • #7
That's right but I would say make sure you get your brackets right. (AB)C_ij is a very confusing notation, when what you mean is (ABC)_ij. ABC is the matrix, and ij indexes an element in ABC, not just C.

Strictly, (AB)C_ij is the matrix AB times a scalar C_ij.
 
  • #8
aaah alright. Yea the notation is a bit of an issue but thanks a lot for your help! I got some more questions but I think I'll make a new thread cos its a bit different :)
 

1. What is matrix multiplication?

Matrix multiplication is a mathematical operation that involves multiplying two matrices together. It is used to combine information from multiple matrices into a single matrix.

2. What is index notation in matrix multiplication?

Index notation, also known as subscript notation, is a way of writing mathematical equations using indices or subscripts to represent variables. In matrix multiplication, index notation is used to specify the location of elements in a matrix.

3. What is suffix notation in matrix multiplication?

Suffix notation, also known as superscript notation, is a way of writing mathematical equations using superscripts to represent variables. In matrix multiplication, suffix notation is used to specify the order of the matrices being multiplied together.

4. What is the difference between index notation and suffix notation in matrix multiplication?

Index notation and suffix notation both serve the same purpose in matrix multiplication, which is to specify the location and order of the matrices being multiplied. The main difference is in the way they are written, with index notation using subscripts and suffix notation using superscripts.

5. Why are index and suffix notations important in matrix multiplication?

Index and suffix notations are important because they allow for a concise and standardized way of writing mathematical equations. In matrix multiplication, they help to clearly specify the location and order of the matrices being multiplied, making the operation easier to understand and perform.

Similar threads

  • Linear and Abstract Algebra
Replies
12
Views
1K
Replies
16
Views
2K
  • Linear and Abstract Algebra
Replies
15
Views
4K
  • Special and General Relativity
Replies
6
Views
1K
  • Special and General Relativity
Replies
6
Views
1K
  • Advanced Physics Homework Help
Replies
10
Views
2K
  • Calculus and Beyond Homework Help
Replies
2
Views
4K
  • Differential Geometry
Replies
4
Views
6K
  • General Math
Replies
1
Views
4K
  • Linear and Abstract Algebra
Replies
2
Views
4K
Back
Top