Let's say we have a matrix $w = [w_1,\ldots,w_k]$ and a set of $k$ bases $\{B_k\}_{k=1}^K.$
I'm wondering - how does
$$\sum_{k=1}^K w_kB_k = Bw \text{?}$$
where $B$ is a matrix of bases vectors $B_i$ and $w$ is the vector above.
I'm confused because, shouldn't it be:
$$\sum_{k=1}^{K}w_kB_k = wb \text{?}$$
Because, if we do the matrix multiplication out, you would have
$[w_1, \ldots, w_k] [b_1 b_2 \ldots b_k]$ where each of $b_i$ are basis vectors. And that would then be equal to the summation, but that's represented as $wb$ and not $Bw$ right? Basically, I'm confused about the ordering here - why $Bw$ as opposed to $Bw$? Or does it not matter?
Thanks!