It's easier to think of matrix multiplication by computing the matrix elements, which means reducing the problem to NM vector dot products.
To get the element of the result matrix at position (n,m), compute the inner product < r_n | c_m >, where r_n is the nth row vector of the left matrix and c_m is the mth column vector of the right matrix. Once you try it, you'll see that it's also much easier to visualize than this strange, unintuitive approach.
With great power comes great responsibility. That domain name belongs to that person. I hope they do society a favor and put more content regarding MM that that, because they chose one of the least intuitive ways of thinking about it. Put more ways up, or ditch the domain.
If the goal is to get people to understand what matrices are, the best way is to teach them about operators, transformations, vector spaces and linear algebra in general, because this is really the only way to fully understand what's going on without relying on some heuristic.
If the goal is to get people to remember how to do matrix multiplication, at least put up more ways of doing it.
I'm sorry if my words upset you. That said, it would be a shame to tell someone off if they bring up a good point (however brash). I used to teach this stuff, and I can tell you many of my students would end up being more confused with your visualization. I hope you can see that you've assumed some responsibility. That's all I can hope.
To get the element of the result matrix at position (n,m), compute the inner product < r_n | c_m >, where r_n is the nth row vector of the left matrix and c_m is the mth column vector of the right matrix. Once you try it, you'll see that it's also much easier to visualize than this strange, unintuitive approach.
With great power comes great responsibility. That domain name belongs to that person. I hope they do society a favor and put more content regarding MM that that, because they chose one of the least intuitive ways of thinking about it. Put more ways up, or ditch the domain.
If the goal is to get people to understand what matrices are, the best way is to teach them about operators, transformations, vector spaces and linear algebra in general, because this is really the only way to fully understand what's going on without relying on some heuristic.
If the goal is to get people to remember how to do matrix multiplication, at least put up more ways of doing it.