6 ms·

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

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.

drdec 11mo ago
I don't understand the down votes, I had the same reaction. Other posters have suggested some better resources, check those out
vixen99 11mo ago
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 https://www.vocabulary.com/dictionary/illustrate
- 0_____0 11mo ago
  It's extremely obvious that the sense of "illustrated" meant here is "containing illustrations."
- sarchertech 11mo ago
  In the context of books or internet books illustrated almost exclusively means “with pictures”.
tptacek 11mo ago
What graphical illustration do you think this is missing? How would that make things better? Have you ever seen http://matrixmultiplication.xyz/ 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).
- griffzhowl 11mo ago
  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
- MaxBarraclough 11mo ago
  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 https://news.ycombinator.com/item?id=41402224 [1] https://www.mathsisfun.com/algebra/images/matrix-multiply-a.svg https://www.mathsisfun.com/algebra/images/matrix-multiply-a.... (from https://www.mathsisfun.com/algebra/matrix-multiplying.html https://www.mathsisfun.com/algebra/matrix-multiplying.html )
  - tptacek 11mo ago
    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).
egonschiele 11mo ago
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 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 https://www.youtube.com/watch?v=LyGKycYT2v0

drdec 11mo ago

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

vixen99 11mo ago

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

0_____0 11mo ago
It's extremely obvious that the sense of "illustrated" meant here is "containing illustrations."
sarchertech 11mo ago
In the context of books or internet books illustrated almost exclusively means “with pictures”.

tptacek 11mo ago

What graphical illustration do you think this is missing? How would that make things better? Have you ever seen http://matrixmultiplication.xyz/ 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).

griffzhowl 11mo ago
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
MaxBarraclough 11mo ago
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 https://news.ycombinator.com/item?id=41402224 [1] https://www.mathsisfun.com/algebra/images/matrix-multiply-a.svg https://www.mathsisfun.com/algebra/images/matrix-multiply-a.... (from https://www.mathsisfun.com/algebra/matrix-multiplying.html https://www.mathsisfun.com/algebra/matrix-multiplying.html )
- tptacek 11mo ago
  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).

egonschiele 11mo ago

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 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 https://www.youtube.com/watch?v=LyGKycYT2v0