I'm given this task:
Rewrite the given matrix summation:
$$ \sum_{i,j,k} M_{ik} O_{kj} N_{jl} v_i $$
Such that the summation begins with the vector v. This is the following answer for this rewritten summation:
Similarly, I'm also asked to rewrite so that we begin with the vector in the summation, given by this answer:
I understand all the actions performed on the matrices within this question but I'm confused with the vector actions. I'm confused about the cases in which the vector's need to be transposed. Why does the vector v not need to be transposed in the first portion, where we rewrite with the vector at the end, however, we need to tranpose in the second situation? Does it have to deal with Matrix row vs column notation? I'm not quite sure in these cases. I appreciate any help, thanks.