Summary
I am looking for a general answer to this question about using $\sum$ or $\prod$ notation for matrices.
Sum
When adding a finite sequence of $n \times m$ matrices, I see that the typical notation is: $$ A_1+A_2+ \ldots +A_k $$
Can I use Sigma notation to shorten this? $$ \sum_{i=1}^{k}{A_i} = A_1+A_2+ \ldots +A_k $$
Product
Similarly for matrix multiplication, when multiplying a finite sequence of $\require{cancel} \cancel{n \times m}$ (EDIT) $n \times n$ matrices can the following notation be used unambiguously?:
$$ \prod_{i=1}^k {A_i} = A_i A_2 \ldots A_k $$ And in the reverse order (because matrix multiplication is not commutative): $$ \prod_{i=0}^{k-1} {A_{k-i}} = A_k A_{k-1} \ldots A_1 $$
EDIT: Per the comments, the ordering is important and can be inferred to be from left to right (thanks @Evariste), as in the general definition on Wikipedia. A suggestion by @Lazy is to explicitly define an index set and iterate on those elements. Would explicit clarity like that help people understand the intention when using this notation?
Prior Research
Because matrix multiplication is not commutative, is associative, and is notated by juxtaposition, then I began to wonder if some sort of notation for concatenation of a sequence would be more suitable than $\prod$ notation
This comment suggests a similar notation but for concatenation, so if I went that route, then: $$ \big\Vert_{i=1}^k {A_i} = A_i A_2 \ldots A_k $$ And in the reverse order: $$ \big\Vert_{i=0}^{k-1} {A_{k-i}} = A_k A_{k-1} \ldots A_1 $$ However, I like that even less than the "$\ldots$" notation for matrices.
Any thoughts?
