yes mhhmmm

? @ForeverMozart

mhhmm yes

@ForeverMozart are you answering my question

@JC574 You're correct, that's precisely what it is.

@AlexClark: It doesn't seem like that formula is too easy to come up with. I have put it into a nicer form, but no luck on a proof.

@MikeMiller i'm confused then, just a sec

Hi @all

What Hom functor do we have here? it's not real linear maps from $\mathbb{C}$ surely

I'm trying to get my LaTeX working, sorry one min

So one functor is $ \mathbb{C} \otimes_\mathbb{R} \underscore $

It's complex linear maps from $\Bbb C$, but you view the output as a real vector space.

AH!

thanks I'll try that

complex

ah so hmm

the tensor is over $\mathbb{R}$

hmm

how many seasons will game of thrones make?

how many

@MikeMiller : Is there any PCA in a metric space?

@MikeMiller if the tensor is over $\mathbb{R}$...

coloring axiom?

@RajeshDachiraju what is a PCA?

coloring axiom

It doesn't make sense to take a tensor over anything but R. One side is a real vector space.

(Principal component Analysis)[en.wikipedia.org/wiki/Principal_component_analysis]

I know neither what a PCA is nor why I'm being pinged about it.

I just pinged hope you know as you are answering some questions here, no problem

What I mean is the Hom should be over the same field as the tensor right? for the adjunction

No, it should not be. You're changing categories...

Look at the statement of the tensor-Hom adjunction on Wikipedia

Ah thanks. For some reason I had it written wrong

this should solve my issue

xx

I just finished my senior year (high school) AP calculus AB course, and I want to learn more math (Yeah, I actually do find math fun). Does anyone know about any free online courses or something where I can learn more advanced stuff?

(I actually know a lot more than what was taught in my calc class, but I don't know notations.

Did you see the message I sent you after our last conversation?

No. I'm looking through the history now

ooh thanks

I'm gonna try to get my hands on a copy of that book

@NemanNasawa If the domain of g(x) is R and it's defined by g(x)=cos(x), then the range can't be (-1, 1]. So the question doesn't make sense, as the function you specify doesn't exist.

If, however, the range is [-1, 1], with a square bracket on the left, then it does exist and it's surjective.

@NemanNasawa Do you know what (-1, 1] and [-1, 1] mean?

unless the domain is (0, pi) or something similar.

Spivak is not the easiest book, but I'm sure folks both here and on the main site would be glad to help with questions.

I looked up Nivan's book, "An Introduction to the Theory of Numbers". Is that the one?

That's the one I was thinking of, yeah.

I read most of it in a Winter break binge in my sophomore year of undergrad.

Would books like that work on a Kindle, or do you recommend getting a physical copy?

Would probably work fine on a Kindle, I don't remember anything that would cause trouble.

Thanks for the recommendation. I have to go right now, so see you later.

Sure, glad to help.

evening chat

h

i