> That's argument from authority, but then: Strang is an authority.

Yes, it's an argument from authority.

> The typical push-pull on a message board is between Strang and Axler

We're not playing Pokemon with linear algebra textbooks here...

> the centrality of the angular interpretation

It's not central. It's one of the ways to think of it. I think 3B1B actually did a good job emphasizing this in his video series: there are many ways to look at vectors, and all of them are sometimes useful. They can be arrows in space, or sequences of numbers, or black boxes that obey the vector space axioms, or polynomials, and so on.

> if your primary purpose for learning linear algebra is to program video games.

What an odd guess. Seriously, I would be surprised if most math teachers didn't mention angles and norms, scalar projections, etc. An important part of math is being able to see things from multiple angles (no pun intended), and this is a useful angle to view the dot product from.

> Linear algebra isn't "about" geometry

Sort of. Linear algebra proper, the study of vector spaces and linear maps between them, is not about geometry, but geometry comes in almost precisely once you equip the vector space with an inner product, such as the dot product. A bare vector space has almost no geometric content, but the inner product gives you lengths, angles, isometries, orthogonality, and all that jazz.

> Strang's teaching goal centers vector spaces and the relationship between spaces.

That's a good goal.

> You need inner products to apply linear transformations with matrices.

I think you have a fundamental misunderstanding of linear algebra here. You do not need an inner product to "apply linear transformations with matrices".

> You basically don't need the angular interpretation... at all? if your goal is to teach linear algebra as a tool for data manipulation

Off the top of my head, cosine similarity? It's not uncommonly used.

But if you're teaching linear algebra for data manipulation, you rarely need the dot product, either. Most "dot products" in data manipulation, like the ones in this article, would be better expressed as row-vector-column-vector matrix products.

> (You need orthogonality, but you didn't say `a⟂b=0`, you said `|a||b|cosθ`).

I said "||a||·||b||·cos(θ) or at least talks about how the dot product relates to parallel and orthogonal vectors". Anyway, it's hard for a person not to interpret orthogonality as a statement about angles, so I'm not sure what distinction you're trying to draw here.

> I'm not rating this blog post "higher" than 3B1B

I guess I misinterpreted "its sauce is stronger", then.

Sorry for any mistakes; this took way too long to type.