Comparing this blog post to a 500-page book or a multi-hour course and calling it “weaksauce” misses the point. This post is meant as an introduction to the dot product, and it does that really well. The formal definition (6.1) and explanation in Axler’s book wouldn’t make a good starting point for most people, it isn't even a good next step in my opinion. It’s great that you’re passionate about the topic, really, but helping more people discover math means meeting them where they are and appreciating content like this for what it’s trying to do.

▲ nh23423fefe 3 days ago | parent [-]

The post contains no geometry. Which is the only worthwhile content of dot products.

Explaining the dot product by its implementation over R^n is pointless. Conflating 1-forms and vectors is pointless.

▲ tptacek 3 days ago | parent [-]

The only worthwhile content of dot products is geometry?

	▲	nh23423fefe 3 days ago \| parent [-]
		of course. dot products are a symmetric form on vector spaces. they let you compute the spheres of radius r. given the sphere of radius r, for any pair of vectors v,w in the sphere `-r^2 <= dot(v,w)=dot(w,v) <= r^2` as w varies from v to -v the value moves from r^2 through 0 to -r^2 this is how we define parallel perpendicular and antiparallel. the dot product is only meaningful in a geometric context. by definition it projects vectors down to scalars. fixing the scalar value finds the spheres, and for a sphere we can vary the vectors to compute cosines.