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This is kind of a dubious question, but is the product notation $\prod$ often used in noncommutative rings?

For example, if $M_i$ are matrices, I guess the common definition of $\prod$ is $$\prod_i M_i=M_1\,M_2\dots$$

but is it also sometimes used as $$\prod_i M_i=\dots M_2\,M_1\text{ ?}$$

If not, is there a common notation for the latter product?

anderstood
  • 3,504
  • No, it is very rare for the big pi notation to be used for products of elements. It is employed for products of algebraic objects, though. It would make good sense to multiply in the order of the indices, left to right, and if the order needs to be scrambled, you could incorporate a permutation into the indices. – rschwieb Oct 27 '14 at 03:30

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