Regarding the product notation... if we have non-commutative things (for example matrices): $$\prod_{i=1}^N {\bf A}_i$$ Is it by default assumed to mean $${\bf A}_1{\bf A}_2\cdots {\bf A}_N$$ or $${\bf A}_N{\bf A}_{N-1} \cdots {\bf A}_1$$ or maybe even an arbitrary order?
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4the first one. Important that the ring/algebra/whatever be associative – Will Jagy Aug 15 '16 at 22:33
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Also related this and its linked question. – rschwieb Aug 16 '16 at 13:20
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@WillJagy why? I'd say it's $((\dots) A_{n-1})A_n$, that's what comes from the recursive definition of the symbol. – quid Aug 16 '16 at 13:48