Someone should convert all the examples into C code so it's more intelligible to programmers who are, let's admit, the main audience for something like this.

To the best of my knowledge: Scalars are variables. Vectors are arrays. Matrices are multi dimensional arrays. Addition and multiplication is iteration with operators. Combinations are concatenation. The rest like dot products or norms are just specialized functions.

But it'd be nice to see it all coded up. It wouldn't be as concise, but it'd be readable.

That's basically what you'll get if you pick up a book on 3D game programming. However, progress will come to a halt when you get to things like determinants and eigenvalues that don't show up in core 3D graphics pipelines. You'll have to find other ways to motivate a C version of that part of the curriculum... but I agree, that's a well-worthwhile thing to ask for.