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This question already has an answer here:

I want to describe a way to express a chain of Dot Product like this:

m[13].m[12].m[11].m[10].m[9].m[8].m[7].m[6]

Something like

comp[i,j]=m[j].m[j-1]...m[i+1].m[i]
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marked as duplicate by corey979, JungHwan Min, MarcoB, halirutan Jun 20 '18 at 0:55

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

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comp[i_, j_] := Array[m, 1 + j - i, {j - 1, i}, Dot]
comp[3, 8]

m[8].m[7].m[6].m[5].m[4].m[3]

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What about

Dot @@ m /@ Range[13, 6, -1]

?

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