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Comment by WrongOnInternet | Hacker News Reader

When I see the word "illustrated," I expect to see graphs or something that would help me visualize how linear algebra works. The only thing "illustrated" about this post is that he hand drew some table which could have been easily with some basic HTML+CSS.

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I think this is a reasonable expectation. I'm writing about the dot product and there is a geometric visualization for dot products, so it's fair to expect that. As I said in this comment (https://news.ycombinator.com/item?id=45802969) I focused on teaching the reader the bare minimum they would need to know to get to matrix multiplication.

I use illustrations for a lot of other things though. I use them to pace my posts, to call out things that are especially important, to reinforce written ideas with images, and to give the reader's eye a place to rest.

If you are looking for graphs, this video about the dot product from 3B1B may be more your speed: https://www.youtube.com/watch?v=LyGKycYT2v0

What graphical illustration do you think this is missing? How would that make things better? Have you ever seen http://matrixmultiplication.xyz/? Great graphical illustration. Also: a really unhelpful way to understand matrix multiplication.

This is part 2 of a series, all under the same name; the first part is extensively illustrated (and I'm not sure the part 1 illustrations are all that helpful).

I agree that's a poor way to teach matrix multiplication. This topic arose last year. [0]

Don't introduce any clumsy nonstandard transformations like 'rotating' a matrix, just highlight the relevant row and column. [1]

[0] https://news.ycombinator.com/item?id=41402224

[1] https://www.mathsisfun.com/algebra/images/matrix-multiply-a.... (from https://www.mathsisfun.com/algebra/matrix-multiplying.html )

I kind of hate all these, because matrix multiplication is easiest to think of as simply repeated matrix-vector multiplication, which you need anyways (and earlier).

Illustrating the dot product using the projection of one vector on another conveys the geometric idea. Then it's transparent why "orthogonal" means dot product = 0.

The author seems to be taking a different tack though, and maybe doesn't want to be too tied to this particular geometric picture

I don't understand the down votes, I had the same reaction. Other posters have suggested some better resources, check those out

That's your preference. However "To illustrate is to make something more clear or visible. Children's books are illustrated with pictures. An example can illustrate an abstract idea. "illustrate" comes from the Latin illustrare 'to light up or enlighten.'"

Quote from https://www.vocabulary.com/dictionary/illustrate

It's extremely obvious that the sense of "illustrated" meant here is "containing illustrations."

In the context of books or internet books illustrated almost exclusively means “with pictures”.

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