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I was thinking of writing: $$\prod_{i=k}^1 A_i$$ But I'm not sure if it is the correct way to do it.

As in: $$\left(A_1{\times}A_2{\times}A_3{\times} ... A_k\right)^{-1} = A_k^{-1}{\times}A^{-1}_{k-1}{\times}A^{-1}_{k-2}{\times} ... {\times}A^{-1}_1$$

I intended to write it more succinctly as: $$ \left(\prod_{i=1}^k A_i \right)^{-1} = \, \prod_{i=k}^1 A_i^{-1}$$

But I'm not sure if it's the correct way of representing it.  
 
 
 
 
 
 
 
 

EDIT

The $A_i$ are matrices.

Community
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Tobi Alafin
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  • It depends a lot on what the $A$'s are. Sets? (So $\times$ is cartesian product here?) Matrices? (So $\times$ is matrix multiplication?) Linear operators? etc. – B. Goddard Jul 09 '17 at 13:01
  • I would like to note that even if a notation is not commonly used, it's ok to use it as long as you define it beforehand (and make sure/make it obvious it's well defined) – Shuri2060 Jul 09 '17 at 13:04

2 Answers2

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It's probably understandable, but not common, to have the indices for the product go in the reverse order. Instead, it would be more common to change the formula for the factors to fix things. You can write something like the following: $$\left(\prod_{i=1}^kA_i\right)^{-1}=\prod_{i=1}^kA^{-1}_{k+1-i}$$

As an aside, if you were worried about the use of $\displaystyle{\prod}$ for the product of matrices, it's in use on Wikipedia, for instance.

Mark S.
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  • It appears, looking at wikipedia capital sigma notation, that common usage is to adjust the subscript, and have the index increment by +1. – CopyPasteIt Jul 09 '17 at 23:31
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Depends on what the object $A_j$ is, but you could use a big $\times$ with limits. See here.

E.g:

enter image description here

user3658307
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