Previously, I wrote a post laying out some rough intuition for tensors.

I made a video where I took the intuition one additional step closer to being concrete

The basic setup is we have a matrix. We then just ask simple questions about the matrix, and see how this “tensor” structure emerges as a natural(ish) idea in the context where

- you change [basis] a lot, and
- want to study objects irrespective of a change of basis, and therefore
- want a data structure that automatically handles basis juggling

I put it in my Abstract Algebra playlist. But you don’t need to watch the first 37 videos to understand it. Reading FQA 4 is probably sufficient. Basic knowledge of linear algebra (such as what the term “basis” means) would help, but you can probably pick all that up from context.

Enjoy!