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.
replyIt'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.
replyYou 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).
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replyThat'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?
replyIt is perhaps addressed to a different crowd?
It’s not okay to be forgetful of maths anymore. Whats a dot product, whats a unit vector, how does matrix multiplication work..
replyI was never actually taught ê as unit vector notation. I did game development for years and am quite familiar with 3D math but a lot of formal math notation is very foreign to me.
replyIt's fine to be forgetful of maths that you're not actively using. (I am speaking as a mathematician.) It's also easier than ever to get a quick reminder or introduction, e.g. for this Google something like [what does e1 with ^ on the e mean], or [standard basis vector] from earlier in the sentence, or ask another AI.
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