Jewel of the whenever: Matrix Multiplication

Eigenchris (I kinda wish I thought of that first) has a series of videos on tensors. I can't give my opinion on the series yet, because I haven't seen them all yet. However, he does something cool that I have never seen before as a mnemonic for matrix multiplication (start at 4:32):

 

We arrange the multiplication as follows. The final product goes in the bottom right. To the left of that, we put the left matrix, and *above* that we put the right matrix. Each cell is then the dot product of the row vector it is on and the column vector it is on

\[\begin{matrix}  & \begin{bmatrix}    . & w_0 & . & . \\    . & w_1 & . & . \\    . & w_2 & . & . \\\end{bmatrix}\\ \begin{bmatrix} v_0 & v_1 & v_2 \\ . & . & \end{bmatrix}& \begin{bmatrix} . & \vec{v}\cdot\vec{w} & . & . \\ . & . & . & . \end{bmatrix}\end{matrix}\]