undefined | Better HN

0 pointscreata7mo ago0 comments

But at the very least, surely a dot product explainer should talk about the two main ways of looking at a dot product! This article leaves out the "angle and norms" (||a||·||b||·cos(θ)) interpretation entirely. It's like if someone gave you the formula for complex multiplication, without also showing you how it's all about rotations.

And maybe I'm being a pedant, but the dot product should be between two things that are in the same space. In the Minnesota lottery example, the probabilities should be a row vector instead. It's the exact same calculation, so again, maybe a bit too pedantic.

0 comments

7 comments · 1 top-level

tptacek7mo ago· 6 in thread

So does Strang! (I just checked, Linear Algebra & Applications 4E).

Also: sir, this is a blog post. It's wild seeing people say "if you really want to understand this topic, pick up Axler". I mean, yeah, also if you were serious you could just enroll in your local community college's Linear Algebra course.

My feeling is that a lot of the critique here is really signaling. For whatever reason, linear algebra is super high-status in this community, and people want to communicate that they've done something serious with it. (I'm sure I'm guilty of that too.)

creataOP7mo ago

> It's wild seeing people say "if you really want to understand this topic, pick up Axler"

I agree. I don't think "Linear Algebra Done Right" is a good fit for most people. It's way too dry, and I don't think his crusade against determinants helps the book. I don't know what a good book suggestion would be, though. Maybe just nab the course notes/slides/exercises off some university's website?

> this is a blog post

Blog posts can be and often are amazing.

> My feeling is that a lot of the critique here is really signaling.

Weird accusation, so just to be clear, I haven't done anything serious with anything, ever.

tptacek7mo ago

I wasn't referring to anybody in particular. But, like: what is the point of calling out a blog post for not presenting the angle interpretation of the dot product? How would that have fit with the goals of this post? You presented it as a defect, but that logic also suggests Strang's explanation is defective.

1 more reply

seanhunter7mo ago

I take exception to the idea that I was somehow signalling, and frankly that's a pretty weird thing to say. It happens that I love maths and am studying it part-time alongside my work. I posted some links to things that I have found useful on my journey so far in the hope that they are useful to others.

tptacek7mo ago

I don't think "taking exception" is helpful. You opened with "If you actually want to learn linear algebra, don't use this blogpost." Do you feel like that really needed to be said?

gnubison7mo ago

Strang does include that. I just checked the fourth edition, like you say you did. Scrolling down two pages to get to the first page of the table of contents, I see the heading “cosines and projections onto lines”. I navigate to that section and it explains all the logic, proof, and intuition behind the connection between angles and dot products. Please don’t spread misinformation…

tptacek7mo ago

That's page 171, 13 dense pages into the section on orthogonality, long after he's introduced the dot product, in a section where he says, in italics, "the orthogonal case is the most important"; he gives cosines about half a page before going back to a perp b.

Nobody said Strang never mentioned cos θ --- that would be weird --- only that his sequencing doesn't treat the angle formula as fundamental, even in the section introducing it. And nobody has ever read Strang and thought projections didn't matter.

j / k navigate · click thread line to collapse

0 comments

7 comments · 1 top-level

tptacek7mo ago· 6 in thread

So does Strang! (I just checked, Linear Algebra & Applications 4E).

creataOP7mo ago

> It's wild seeing people say "if you really want to understand this topic, pick up Axler"

> this is a blog post

Blog posts can be and often are amazing.

> My feeling is that a lot of the critique here is really signaling.

Weird accusation, so just to be clear, I haven't done anything serious with anything, ever.

tptacek7mo ago

1 more reply

seanhunter7mo ago

tptacek7mo ago

I don't think "taking exception" is helpful. You opened with "If you actually want to learn linear algebra, don't use this blogpost." Do you feel like that really needed to be said?

gnubison7mo ago

tptacek7mo ago

j / k navigate · click thread line to collapse