OH GOD, NO!

Commutative diagrams are the DEVIL!

THE POWER OF CHRIST COMPELS YOU!

THE POWER OF CHRIST COMPELS YOU!!!!

hi @XanderHenderson

I hear certain shittalking about my diagram

As a representative of a commutative diagram, yours is perfect

the only problem is that commutative diagrams create a home for SATAN

and you don't want that, do you?

Commutive diagrams are awesome

lol

i need help

ask and wait for a savior

SAVIOR PLEASE HELP ME

The only salvation is within ourselves

im fked then

Sigh... I need to be more careful reading the reasons that edits are made...

lol

still mad at you @XanderHenderson

Why, Faust, why?

I should not have rejected this edit...

you voted to close one of posts for a retarded reason

and left no comment

Which post?

And in voting to close, I clicked a box that left a comment...

and if you get one close vote on the retarded site the question will be closed within a week even if you edit it

Well, give me a link... if it is better, I would be happy to vote to reopen

too a week to close was reopen in 10 minutes

i could find it it got reopened a long time ago

okay, so... I don't understand what the problem is?

t comments if you think a post is missing something

i cant find it was topology question froma couple months ago

oh i can findhttps://math.stackexchange.com/questions/2649829/countable-topology-on-0-1

the answer is wrong lol

you voted to close it for lack of info from OP but didnt put a comment to what was missing

makes it hard to figure out wtf is missing

anyway thought we were friends if you dont like one my posts tell me what you want in it and ill try hard to fix it :P @XanderHenderson

Honestly, I don't remember that question. In a typical day, I cast a lot of votes (both from the review queue and otherwise)

Looking at the question now, I am surprised that I did not vote to close it as "overly broad"

I can make a good case for leaving it open, too

You really oughtn't take it personally---I rarely even notice who is asking the question

originally i only asked about the third part but someone said there wasnt enough info so i answered the other two parts.

:p

That is not immediately obvious from the question, which looks like maybe a question about proof verification?

originally i had an incomplete argument for the third part was trying to figure out how to do it so i posted as a question. then some doorknob posted a wrong answer that got a ton of upvotes cause people are retarded

just for the record, I'm not a fan of slurs like "retarded"

its still somehow got +2 votes despite being completely incorrect

That happens a lot

i have 6 learning disabilities if someones allowed to call someone retarded its me.

My brother has Downs Syndrome, complete with IQ hovering around 70

my brother-in-law also had Downs Syndrome, until he died of a brain aneurysm that was likely related to a malformation of his heart

my condolences life sucks.

which is common in people with Downs

the point is, "retarded" is a slur that you really oughtn't use, regardless of whether or not you feel like you have the privilege to do so

similarly, despite the fact that I am Jewish, I wouldn't throw around the word "kike"

its a word that has different meanings to different people it was not my intention to communicate ill feelings merely to emphasis the ridiculous of someone leaving an incorrect answer after having it explained by several individuals to be incorrect. normally i don't have a problem using it as mentally im a large disadvantage compared to the average person but it was not meant to communicate offence merely to illustrate a point.

sorry to offend you i am autistic i realize i should apologize as i have likely offended you but i am not particularly well versed in the process of doing so in the correct manner.

I have this statement: Let $G$ be a group, $S = \{ x \}, Z_n = \langle x \rangle$, and $\overline{\varphi} : S \rightarrow G$ a set mapping. Then $\overline{\varphi}$ extends to a homomorphism $\varphi : Z_n \rightarrow G$ if and only if $\overline{\varphi}(x)^n = 1$. But I don't know what 'extends to a homomorphism' means, please explain! (I have proof of statement.)

the orgional map is a map from the set S to the set G

its saying that if you extend the map to the structure of the groups and it becomes a homomorphism

a homomorphism isnt just a map its a map the preserves some of the structure of the binary operation

@XanderHenderson

@Silent the requirment in the iff statement also makes alot of sence its saying that if you take the map to the order of the group it must equal the identity this must be true for any homomorphism and is easy to prove

MOrning ted

yeah making an ass of myself

Oh, as usual :)

pretty much.

i have a question

Yeah?

where $T*$ is the adjiont

i feel stupid but i have no idea how to start either direction of this

I haven't seen that before.

wierd question right?

No, it seems like a good characterization. Can you do it for self-adjoint and unitary?

my confusion is i see no relation between any polynomal cept the characteristic or minimal polynimal or something in Ann(T)

That's why I asked you if you can see it for the two major cases ...

You know the spectral theorem for normal operators, I assume.

no i cant

yes

Self adjoint means?

i belive the spectral theorem is needed for the hard direction

$T=T^* $

So what's $f$?

theres my confusion i have no idea what a correlation or than caley hamiltion has to do with T or $T^*$

other*

hi y'all

No Cayley-Hamilton. If $T=T^*$, then how do you write $T^*= f(T)$?

heya Joe

lmao

let f(x)-x

f(x)=x

OK, now what about unitary?

unitary can use cayley hamilton

Right.

So can we do this if $T$ is diagonal?

I actually don't see that in general.

hmm

if we could do it for diagonal we could get one direction

The hard direction. The easy direction really is trivial.

I don't see how to write $\bar\lambda$ as a polynomial in $\lambda$.

I mean, I know I can't.

use he spectral theorem and that?

Oh, I'm being silly.

I need a polynomial that will work for all the eigenvalues.

usually when we are asked to prove something wierd its needed for the hard question

Oh, definitely need the spectral theorem to unitarily diagonalize. But then it reduces to what I asked.

Do you see why the easy direction really is trivial?

hi @MikeM

no :(

$T$ commutes with a polynomial in $T$.

stupid question -- what would D(deta(A)) look like?

:(

@JoeShmo: Have you done this at the identity for starters?

nope

thats really not fair ted

I never said I was fair.

so you think that extra result i proved is unrelated?

No, you need it for the hard direction.

what do you use it for?

Take a diagonal matrix with entries $\lambda_j$. What is the adjoint?

the matrix with $\lambda_j $ bar as its diagional entries

sorry dont know how to put the bar on top

Right. So you want a polynomial that turns one matrix into the other.

just \bar

but ones amtrix and ones an operator.

aw come on.

evidentatly im missing something obvious

By this point you should understand how to go back and forth.

is there significance to the fact that det is a linear functional on M_n(R) btw?

Hmmm, Joe ... VERY NOT linear.

so i write the diagonal matrix as an opertor

multilinear, yes.

@Faust: Go backwards. Find a unitary basis that will diagonalize your operator.

multilinear* functional

what is it?

(the significance)

Guess you need to watch my lectures on determinants, Joe.

sorry almost there ( i missed alot of calsses from being the hospital so many times and learned all this from the textbook)

no i understand determinants

i mean im not saying i shouldn't watch your lectures anyway

They're functions of $n$ vectors (e.g., the columns), linear as a function of each.

:)

im glad u understand determinats i sure as hell dont

wait why not

so i use the spectral theorem to find a orthonormal basis

um, how's this -- determinant is the factor of change in volume

how come you can use such fancy terms freely but you don't understand determinants?

yeah, not so relevant at the moment, Joe.

Huh?

referring to Faust there ^

@JoeShmo learned linear algebra form a textbook that doesnt use determinates

A textbook of which I'm rather not fond.

now thats the most interesting thing ive heard all day

But it has some good stuff in it.

i under stand the a bit goemtrically

how do you circumvent detA?

good series

Plus the author is as opinionated as I am and says his way is "done right."

sheldon axlers book

he covers linear algebra at a reasonable level for a second course in linear algebra w.o determinates

interesting

but i do understand them a bit geometrically

the existence proof is pretty neat

I'll probably prefer my own videos, @orbit.

the determinant is the unique multilinear (....i forget the rest. the hour is late. @TedShifrin?)

@Ted, not to knock your videos, but these are absolutely fantastic.

he has other great math videos as well

great channel

surprised you haven't heard of him

the determinate is an idea of the streching of the n dimensional space

Who is he, @orbit?

for example in R^3 its measure of the distrotion of volume

bascially you would go about describing a function that describes a factor of a change in volume in linear algebraic terms, and proceed to constructively show it's unique

if the determinate is zero it means your soltion space is one or 2 dimensional

hence the 0 volume

signed volume, of course, guys.

He did his undergrad in math and cs at Stanford. He makes math videos on youtube now. That's all I know of him. His name is Grant

signed, signed.

@TedShifrin explain to me the negative volume

IF you reverse orientation, @Faust.

Flip

perhaps its the downward direction of volume?

Try the matrix $\begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix}$.

No, no.

i was being an asshat

@JoeShmo whats intresting is finding eigenvalues w.o using the determinate

asshat usual.

^^ sorry

@Faust: it's really not that interesting. It's just the module-theoretic way of thinking of linear operators.

how indeed?

i have learned one thing module is much better way of thinking about linear algerbra

Look at the ideal of polynomials annihilating your operator.

looking forward to the day i maybe smart enough to take a class on it

The minimal polynomial generates the ideal. The characteristic polynomial is in it (by Cayley-Hamilton).

because of being sick i am still 4 semester away from graduating :( not going to have enough undergrad amth classes to take at my uni

I didn't realize you'd become so sick, Faust. I'm so sorry.

thats cause its a PID

ended up in the hospital 3 times in the last 2 weeks

What have you done to yourself?

what's going on?

had to go down to 2 classes for the semseter

was advised to withdraw completly by my doctor

but id lose my scholarship if i did

Generally one should not ignore doctors.

Ah.

I bet you could appeal with the doctor's letter.

and free money ^

not permanently but for the semester and it was 5k so im sucking it up without being able to make it to many classes

they let me keep the money with only 2 classes because technically im disabled

but still gunna cost me a whole nother semester :'(

which university do you go to?

is this in the states?

University of Victoria in Victoria Bc canada

woaaaaah

dude

im at ubc

haha, small world

@DivyankaS.Chaudhari: Did you just list all the options?

@DivyankaS.Chaudhari order clearly matters

Have you learned about generating functions?

@orbit-stabilizer you doing math?

@Faust, yeah. Math + stats

I don't see anything to do with permutations and combinations.

nice im doing math

How's UVic?

i like it but im an island boy

What does that mean?

i was born on vancouver island and lived here most of my life

its a fairly common term around bc...

being form "the island"

You can do it systematically by considering the number of $2$'s, I bet, @DivyankaS.Chaudhari.

Yeah, I've heard it - but I wasn't sure what it meant.

were generally considered eccentric west coasters shorts t shirt and toque people, most people form the island live most of there lives on it

or 0 times.

Theres actually tons of people on this stupid rock that have never actually left it before

Ugh.

I vote for generating functions.

generating functions best way to do that question

normally textbook deifnt he sequence with a generating function

my textbook on combinatorics does

Which year are you in?

Uh huh.

think theres a one to one correspondence between those numbers and the number off odd somethings for the same number

Fuast

Faust*

@orbit-stabilizer im technically year 3 but i have all my math courses after this semester just need credits to graduate but i could literally take anything i wanted for them

Nice, what are the core courses you have to take at UVic? Is there a bullshit ODE and PDE course there?

I hated our BS differential equations courses

i have taken a few ode classes would only call one of them bs

never taken pdes

but probally will

Idk how I passed my ODE class , didn’t even open the book

my third year odes class easiest 3rd year class i ever took

i literally just drew pictures of stuff

of and maybe something to do with a taylor polynomial