@Leaky: Actually, embedding the affine group into the general linear group one dimension up is very important.

I see

Computer graphics people use this everywhere, not surprisingly.

@TedShifrin thanks ppbut I understand it from practice (I’ve been doing matrices for a bit now) just trying to conceptualise the idea

@JakeRose did you try my exercise?

(exercise as in, moving your body)

Conceptualizing is exactly composition of functions. As I wrote, $(AB)x = A(Bx)$, so you first do $B$ then do $A$. No reason it'll be the same in the other order. You know that from basic functions, too, as I illustrated. $\sin(x^2)$ is very different from $(\sin x)^2$.

@LeakyNun no but my cat did. You owe me a gravestone because I live on a second story and the window was open

your cat did me :o

LOL gives points to Jake

...

editing because you hit send spoils the greatest internet jokes

@LeakyNun I do get your argument though

it spoils the not-so-great ones, too

I often send messages while I'm in the middle of typing a contraction

Actually, my matrix $A$ works with Leaky's rotation matrix example, doesn't it?

because I hit enter instead of '

$A$ reflects across the diagonal $y=x$. If you rotate and reflect, that's quite different from reflecting and then rotating.

You can draw pictures !!

@micsthepick: They should redesign the typewriter keyboard.

well, there have been attempts

@TedShifrin But the levers would get tangled more often if they did that

The following post is mine: math.stackexchange.com/questions/2895528/…

@TedShifrin The author Takashi just put a book link in the post

and it had several comments that just disappeared

is there away for me to find out why?

@Bob diamond mods prune irrelevant comments

you can ask them why in the mod chat room if it matters

I thought the comments were very relevant

@Bob i guess they didn't.

Some like to keep comments to just the maths and related matters

They were related to the math posted and my errors

@RobertFrost thanks for the help and have a nice day ; bye

@Ted what would you say is a good overall distribution of schools to apply to? In the sense of, applying to n of the top folk, m mid-level, etc