The very first formula in the text, explicitly described as "as simple as possible," names its variable ê1 with no explanation given. I think this paper needs another pass.

It’s not okay to be forgetful of maths anymore. Whats a dot product, whats a unit vector, how does matrix multiplication work..

What do you mean "no explanation given"? It says: "In 2 dimensions, the standard (or identity) basis vectors are ê1 = [ 1 0 ] and ê2 = [0 1]." Seems pretty clear to me he's defining ê1 and ê2, or rather telling us that he's using this very common way of naming the basis vectors.

It's just giving a vector a name. It also names ê₂. These particular names are very standard and familiar to most people who've met vectors before.

You can look at those vectors and see that the position of the 1 is the subscript, without explanation. The ^ could do with an explanation that it means unit vector, but if you've met vectors before you likely know that (maybe that's elsewhere in the book, but a quick search didn't find it).

That's absolutely standard notation for a unit basis vector. I haven't read the prerequisites carefully, so if it addressed to the general public maybe?

It is perhaps addressed to a different crowd?