The key is to picture \\(A\\) as a matrix of row-vectors and \\(B\\) as a matrix of column vectors.

Here are the rows of A:

\\[
A
=
\begin{bmatrix}
\text{---} & a_1 & \text{---} \\\\
\text{---} & a_2 & \text{---} \\\\
& \vdots & \\\\
\text{---} & a_m & \text{---}
\end{bmatrix}
\\]

Here are the columns of B:

\\[
B
=
\begin{bmatrix}
\vert & \vert & & \vert \\\\
b_1 & b_2 & ... & b_n \\\\
\vert & \vert & & \vert
\end{bmatrix}
\\]