@Pedro I don't know yet. I want to talk about the geometric interpretation of the determinant, but that can't fill an hour.

@Mike Ah.

Why not talk about alternating forms.

And why the determinant is unique by looking at the dimension of the space of alternate $k$-forms.

That will probably be too hard for them. It's mostly a class of first-year engineers.

@Mike Oh, drats.

hi @WillHunting

IT WORKS!!!!

@Charlie Hello. You are doing linear algebra?

the program works!!!!!

@WillHunting nope

@Charlie Well, $$M-I=\begin{pmatrix}0&0&1\\0&0&0\\0&0&0\end{pmatrix}$$

@PedroTamaroff yes...

@WillHunting hi jasper :)

That has rank $1$.

Quick question, I had a homework question which has two planes, and then I had to find the volume in between them given a few constraints, is it possible for the volume to be zero if the planes are on top of each other?

@meer2kat Hi. You woke up so early

yes dear @pedro

Hence its kernel is $e_1,e_2$.

Nothing more there.

The matrix is not diagonalizable.

@Link as in they intersect at every point?

@meer2kat yes.

@PedroTamaroff i know, pedro,but there's a way to find a third

@WillHunting really? i've been up nearly four hours

@Charlie Take a sum of the other two?

@PedroTamaroff it's a problem from differential equations

@Link that would essentially make them the same plane, so yea

@Charlie Oh.

But then you want the Jordan form.

@meer2kat all right, thank you ^^

@meer2kat Yes, that's what I meant. 6.30 lol

@PedroTamaroff yes, basically

@WillHunting stalking me :O knowing when i woke up

@Link no problem, zelda fan ^-^

@meer2kat Well, I just read the transcript lol Yes, I have been called a stalker before on SE

@Charlie Do you know the algorithm to find a Jordan basis?

@WillHunting XD hahaha

@PedroTamaroff i don't remember

@PedroTamaroff my best friend is jordan. her basis is awesomeness.

@Charlie OK. Let my try to write things out.

@meer2kat That is so lame

@WillHunting Jasper is bitchy today.

@WillHunting um no. that is not part of the algorithm

@PedroTamaroff he is indeed

Thanks for starring, now I appear on the starboard, yay!

@WillHunting lol

@WillHunting how is everything goin' jasperrr?

@Charlie I am a little better, but not much

@Charlie OK. Bear with me here.

okay @pedro

@meer2kat Do you have morning classes today?

@WillHunting I'm not in school this semester.

@WillHunting I'm at work.

@meer2kat Oh, then you shouldn't be talking lol

@WillHunting meh

@Charlie So, we have $\ker(M-I)=\{e_1,e_2\}$, $\ker(M-I)^2=\{e_1,e_2,e_3\}=\Bbb R^3$.

@WillHunting not a big deal.

@PedroTamaroff yupyupyup

Any way to make this mess more readable?

I missed the $\langle \cdot \rangle$. Sorry about that.

@Charlie So $\{e_1,e_2\}$ is a basis of $\ker(M-I)$.

yes, it is

Now, we can extend this to a basis of $\ker(M-I)^2=\Bbb R^3$.

By adding $e_3$.

@meer2kat So what did you paint over the weekend?

Err... sorry. I shouldn't be making things so complicated.

@WillHunting never got around to it. SHK kept me busy :(

@meer2kat I suppose that is your online game. Computer games are boring. I almost never played them

@WillHunting I strongly enjoy video games. Yes, Stronghold Kingdoms. A great combo of slow and fast paced, endless layers of politics and wars and fighting, and constant room for self-improvement in the game's natural hierarchy, while leaving ample time for social interaction, communication, and bargaining skills. I love it.

@PedroTamaroff I didn't understand the prof's explanation either

@WillHunting it's a game that takes a lot of patience. not too many young people play it.

For some reason it's not working

@meer2kat So you go back to classes next semester?

@Charlie What course is this if it is not linear algebra?

@WillHunting not until fall. couldn't afford summer term.

@meer2kat Ah, so you are working to get some money for school?

@WillHunting differential equations

@Charlie Ah, Gerald Teschl's book is very good

@WillHunting yes. and it was part of my curriculum. i'm at an engineering company.

@WillHunting I'm using smale, devaney & hirsch

@Charlie OK, that's an easier book. Smale is a Fields medallist

@WillHunting I know

Wait.

@meer2kat Hmm, in the university I went to, the attachment to a company takes place only during the final year of studies

Hi @Jas

@will I mean

@user127001 Hello Bart

@Charlie I never took a course in differential equations, but they are needed in the study of differential geometry

@Charlie Well, I claim your Jordan base is $\{e_1,e_3,e_2\}$.

@WillHunting it's a very appied subject, so we must know it

So your JNF is $$\begin{pmatrix}1&1&0\\0&1&0\\0&0&1\end{pmatrix}$$

Really @will? I am taking differential geometry next semester and I don't even know what differential equations are

@user127001 OK, there are large parts that can be done without differential equations

@PedroTamaroff yes, yes, makes sense, pedro

@will Will I be okay for intro differential geometry

@will the pre-reqs only say multivariate calculus

@user127001 Well, I don't know what you are good or bad at. Just do your best

@will I am bad at everything

@user127001 Oh dear. At least finish your degree

@PedroTamaroff thanks , Pedro

@WillHunting we do three semesters. every other semester starting spring of sophomore year

@meer2kat Wow, that's a lot. Anyway, I guess it won't be of much use if you are going to change major to math

@WillHunting lol! it's okay :)

:D

@WillHunting good money, good fun

@MickLH hiiiii

@meer2kat At least you get the money, yay!

@meer2kat heyyy

@WillHunting exactly

@meer2kat That's a lot of i's, lol

@MickLH sup

@WillHunting anddddd? :P

@meer2kat Well I'm trying to figure out what I was coming up with last night

@MickLH reagrding?

I was trying to come up with an efficient way to evaluate $\psi_{n}(x)$

@MickLH What function is that?

i'm trying to provide answer for math.stackexchange.com/questions/753368/… but i can't

PolyGamma

formatting...

how to type sqare root

I got a lot of work done last night... on "the other side" at whatever crazy hours of the night

But I didn't make any notes :'(

@MickLH nice

@AvinashRaj \sqrt {}

Now I'm trying to trace my steps and figure out why one tab group trails off into research about Bernoulli numbers

I am trying to look at e^{ix^2} and the maximum value it can take for $R e^{i\theta}$, $0 \leq \theta \leq \pi/4$. Any ideas?

$(x^2+y^2+z^2)=sqrt {x}$

is this correct?

@meer2kat I am going back to bed. I will see you in my dreams lol

$C_2 = \{ z : z = Re^{i\theta}, 0 \leq \theta \leq \frac{\pi}{4} \}$

Then I am stuck, lol

@meer2kat your avatar really reminds me of him

@N3buchadnezzar "I am mathing, but then I can't."

@Charlie umm....okay.... :(

@PedroTamaroff I want to say that the the $C_R = C_2$ goes to zero as $R$ goes to infinity. But it seems the supremum is $\cos R(R-1)$, which is gay. Since that is undefined as R grows

Silly math, why are you so silly

:(

:(

:(

@user127001 :( @Charlie is mean :(

cheer up muthafuckas!

@Pedro Makoto Kato is disingenuous as hell.

@N3buchadnezzar Start over, I missed everything.

@Mike Yeah, he's not liked here.

He was suspended a few times, I think?

@PedroTamaroff ?

@Mike Too much?.

Do "they" make organic reeses puffs yet?

yes, cocoa comes from an organic life form

@Pedro He's got into some meta drama now because he posted a question that was really lazy. They deleted the meta questions though.

@Mike You know full well that I mean made of materials reduced from inputs created by genetic sequences developed through evolution as opposed to intelligent design

I have to go offline for a few hours. BBL

peace!

@MickLH Well, since God created the world, all things are intelligently designed. I'm not sure what your issue is.

@Mike I think humans aren't quite as skilled as god at writing up new pieces of DNA, maybe luckier but I'll take a slow reliable method over an unstable approximation

So you prefer things made by man, as you wouldn't call those intelligently designed?

lol

While that appears very contradictory to my intended point, it's ironically true in some other aspects

@MickLH Unstable approximations, like Maclaurin for $\ln (x)$ ?

@Mike Dang, I missed the drama.

@FernandoMartin ?

@PedroTamaroff You found it.

@Mike ORLY.

Well, you just voted to close the question that spawned the drama.

You said it was beeleted.

The meta questions he posted about it are.

First one was "Why was this question closed?" where people rehashed the same arguments as usual.

Then when that was closed we got "Why was this meta question closed?"

Then when that was closed he posted in the "request to reopen" thread, then posted a thread requesting votes to reopen his question.

@Mike SIGH.

meta.meta.meta.stackexchange....

That question is especially obnoxious because it's trivial. It's obvious from the start that he had intended to post the standard proof (for some reason).

@Mike Many people already suggested he started a forum. =D

Of course, he won't do it.

:(

I honestly don't get why he does this.

@KhallilBenyattou for some reason, this comment led me straight to a great optimization idea

I often resort to using series for some of the "core" functions, but it's silly to do arbitrary precision exponentiation and then evaluate the series for $ln(x+1)$, when the series for $ln(x^n+1)$ could reach the answer directly

@MickLH That was lucky! :D

yayyyy lunchtime

@meer2kat What time is it where you are? (In the UK it's 5pm)

@KhallilBenyattou She is in Midwest.

Hi, a curious question: what is the dimension and basis of quadratic forms over R? Is the dimension one and basis any real number?

Sorry, that about basis is nonsense... But what is the basis?

how many variables do your forms have?

Well, they take in a vector from corresponding vector space

so $n$ where $n$ is the dim of your vector space

@Sawarnik kya ?

@r9m Kuch nahi. Are you busy?

@Sawarnik no ..

@r9m I found out that higher maths is very tough :(

@Sawarnik What's higher maths?

Do you mean undergraduate level maths or postgraduate level?

@KhallilBenyattou Undergraduate level.

@Sawarnik

Oh, so you're currently doing an undergraduate degree?

No, fortunately :)

@Sawarnik Is that next year?

@KhallilBenyattou At least 4 years now :)

@KhallilBenyattou 12:30 PM

@Sawarnik ORLY ;)

@meer2kat You have lunch so early?

@KhallilBenyattou Maybe, not sure. But if I will, then its 4 yrs :)

@r9m Yes! :'(

@Mike OK, thanks, and what is the basis? Is formed by quadratic forms which assign 1 to corresponding vector of a basis of the vector space and zero to all the others?

@Sawarnik why are u worrying about that now ?

@Sawarnik Are you currently doing an undergraduate degree or are you still in school? I'm curious as stackexchange is pretty advanced stuff for maths at the very least :)

(I'll be starting my first year of undergrad in September/October!)

@KhallilBenyattou yes, this is me

@KhallilBenyattou Of course I m still in school :)

@mirgee no - it's got dimension $(n^2+n)/2$. Let's say our vector space is things of the form $a_1v_1+a_2v_2$

@Sawarnik that's midday to us. i eat lunch sometime between 11am and 1 pm

then the basis is $v \mapsto a_1^2$, $v \mapsto a_1a_2$, $v \mapsto a_2^2$

@Sawarnik btw did you check the solution for the ineq problem ? Macavity posted a link .. must say they slew a dragon :P

uhoh @enjoysmath is here....hide guys!

@r9m Yup!

@meer2kat Why?

@Sawarnik he's scarrrryyyy :P

Yes, smart people like me can seem alien and scary sometimes

@KhallilBenyattou thanks khallil :)

@Mike: Are you sure? Quadratic forms are maps V_n -> R

@EnjoysMath I think he just called the rest of us stupid XD

@KhallilBenyattou Why does everyone say the same?

@Sawarnik do you disagree?

@r9m Where did you get the problem btw :)

@KhallilBenyattou yay for 19 yr olds! woowoo! represent

@Sawarnik my room mate was teasing me with the problem .. lol

@r9m Were you able to give him a reply? :p

@meer2kat not sure.

@Sawarnik lol that's okay. :P

@KhallilBenyattou ah you're a little younger than me. sadly, 19 is almost gone for me. great age though. it's a good time

@Sawarnik he looked it up from AoPS only ..

@meer2kat Wat! You are only 20 or thereabouts!

put that in your ear hole

@Sawarnik i'm not even 20. i turn 20 in a little over a month. why? do i look older or something?

@meer2kat No, you have a bachelor degree, and you have a job. That doesn't fit with a 20 year old?

@Sawarnik i don't have my bachelor's yet. i could have one in...about a year. but i'm going to spread it to 1.5 years.

@Sawarnik i'm a co-op. it's like...an apprenticeship

@Sawarnik but yeah..i should have my bachelor's and my master's when i'm 22

she's a cop... run! :O

@meer2kat My brother only has a bachelor and he is 22. I'm surprised.

@EnjoysMath co-op smartypants

@Sawarnik what's his degree in?

@meer2kat BTech.

@Sawarnik wow .. you have a bro ?

@Sawarnik hmmmmm

@r9m Plus a sis :)

I thought you meant "cuwop" like a new york accentuated "cop"

@Sawarnik even better (y)

it's fine if you're a cop though, I was joking

@EnjoysMath lol no cooperative education.

@EnjoysMath nah i'm not a huge fan either

@meer2kat Does this mean that you're really smart?

:)

@KhallilBenyattou Yes, she is!

What's coop education?

@KhallilBenyattou i think i'm smart :P but no, i just started college as a sophomore because of advanced placement credit

@EnjoysMath enjoys being hand cuffed ?

:P

@Mike What do you think?

to the bed?

um

@mirgee Yes, they are. But they're not arbitrary maps.

@EnjoysMath it's when students work at real companies for money and essentially learn about the industry

@Mike Yes, they are restriction of bilinear forms

what evil coorperation do you work for now?

@meer2kat That's pretty cool! I showed glimpses of being smart when I was younger. Now on the other hand, I'm pretty slow ^_^"

@EnjoysMath GKN Sinter Metals. Actually a UK based company

@KhallilBenyattou You outlined my future!

@KhallilBenyattou hahaha :D

Do they cast brass parts for prototypes?

@EnjoysMath they use compact pressing and sintering to create automobile parts

oh, I need a company that does small orders for a prototype of small parts: custom guitar tuning handles with a gear designed into them

but that's cool, I'll just take my business elsewhere

:D

@EnjoysMath sounds like you need a 3d modeling company. or injection mold specialists. if you need help with injection molding, i actually do freelance injection mold tool design

@meer2kat What's your charge?

@Sawarnik i'm flexible

@EnjoysMath are these single prototypes or something you want to create a lot of?

I need to do the 3D modelling for it myself in FreeCad, but I need to order like 12 for prototypes, then later a crapload

maybe more for prototypes once I make the prototype pristine

@EnjoysMath oh okay. i can't help then. for what i do, i create 3d models for the things. what part of the country are you in?

@meer2kat Do you mean to sound that seductive in my mind when you say "I'm flexible"? :P

I will probably 3D print the plastic parts

@KhallilBenyattou i actually am physically flexible as well but that was not the point.

@EnjoysMath yeah. you have a 3d printing place near you?

o__o

there are services online for doing that or my office might get one for 500 bux

@EnjoysMath nice. good luck then.

@meer2kat Oh, good, will you work for free?

@meer2kat It's my hormone driven mind -_-

@Sawarnik not quite that flexible (usually)

@KhallilBenyattou i understand. my mind is always in the gutter XD

@Mike Im so sorry to bother you, but what did you mean by "things of the form $a_1v_1+a_2v_2$"? There might be squares of the coordinates as well...?

@r9m Was the one answer to your q given correct?

@Sawarnik I saw that comment. Cheeky!

nice save @sawarnik lol

@meer2kat You saw it too haha!

@Sawarnik no ..

@KhallilBenyattou yes i did hahaha