That's a cartesian product, not a tensor product.

the outer product is the tensor product of two vectors https://en.wikipedia.org/wiki/Outer_product

Could that be the start of an introduction to tensor products or even tensors in general ? Start with cartesian product ( or maybe even sql joins ? ) and generalize ? It's probably much more intuitive to us developpers than vector products ( unless you're in 3D graphics or physic engine of course )

I'd read an article like that.

absolutely. I am doing a minitature sql join.

other database operations may have similar interpretations in terms of vector spaces.

math - when it works - is a layer of abstraction unifying several different-looking experiences.

I think it might be a bit more correct to call it the outer product.