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I am considering a product of the matrices $(A_i)_{1\leq i\leq n}$ in reverse order $$P=A_nA_{n-1}\dots A_1,$$ and I was wondering if there was a standard notation for it, like $\overleftarrow{\prod}$ or $\prod^R$... Thanks

Tom-Tom
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    I like $A_nA_{n-1}\cdots A_1$... – JP McCarthy Apr 27 '15 at 10:32
  • @JpMcCarthy. Sure, my point is whether there is another one I could use to lighten the text. – Tom-Tom Apr 27 '15 at 13:49
  • I know that... perhaps the best thing would be if you are using this product multiple times to write something like "denote $A_n\cdots A_1$ by $\displaystyle \prod_{i=n}^1A_i$". Then there you are covered and can use the notation wherever you want to refer to the product. – JP McCarthy Apr 27 '15 at 15:26

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I don't think there is such a notation.

However, you won't need it, as you can do the following product:

$$\prod_{i=1}^n A_{n-i+1}$$

or equivalently

$$\prod_{i=0}^{n-1} A_{n-i}$$

naslundx
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    You believe then that it is clear for everyone the $\prod$ symbol stands for product to the right ? – Tom-Tom Apr 27 '15 at 10:18
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    @Tom-Tom Products are usually assumed to be left-associative. – A.P. Apr 27 '15 at 10:33
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    I also thought about $\prod_{i=n}^0$. However, if there is no widespread notations, I'll use whatever I like best. – Tom-Tom Apr 27 '15 at 11:49