Mathematics - 2012-06-15 (page 2 of 4)

Frank Science

10:00

OK, maped.

math.ucla.edu/~robjohn/math/mathjax.html

Question:

What's rendering off and rendering on?

@anon

robjohn

10:15

@MartinSleziak Get 'em while you can. Once you're at a certain reputation, you can do those edits without review. Then you don't get any points for them. You can get points for Tag Wikis up to 20K, but at 2000, you can do regular edits without review.

user19161

@FrankScience It just means whether the conversion is turned off or on.

Frank Science

@JasperLoy

?

skullpatrol

@robjohn My negative/minus question has been down voted five times since I added the two links. It looks like skullpatrol is going out in a blaze of glory!!!

experimentX

@FrankScience having problem with latex

??

Frank Science

No, my problem is about math.ucla.edu/~robjohn/math/mathjax.html

"on" and "off" seems no effects

robjohn

10:20

@skullpatrol It's CW, so downvotes don't remove reputation, though.

J. M.

Hi rob.

robjohn

@JM Hey there! how are you today?

J. M.

Just got my swag today. :)

The mug is huge!

user19161

@skullpatrol Congrats!!!

robjohn

@JM Cool! I got my swag a week or two ago, and then came the shirt and pens for being in the election. I had forgotten which color shirt I got for the former and ordered the same for the latter. I now have two white MSE t-shirts.

user19161

10:23

@JM You may share the coffee with us.

robjohn

@JM It is pretty big :-)

user19161

@robjohn Ah you get stuff for elections too!

robjohn

@JasperLoy Yes, it's the same swag, minus the mug.

J. M.

@robjohn They sent stuff to candidates too? Wow.

@JasperLoy Nah, I can use being buzzed for a whole day... :)

experimentX

I'm having problem on transformation of unit vectors?? from one coordinate sytem to another .... can anyone provide me with any link??

Frank Science

10:25

Can I use another typeface, such as AMS Euler in MathJax?

robjohn

@JM I got a comment from t.b. today :-)

user19161

@experimentX Read your textbook first.

experimentX

Not in my textbook ... only for coordinate systems

robjohn

@experimentX Depending on the new coordinate system, they may no longer be unit vectors.

experimentX

I mean there's for rectangular to cylindrical ... but not from cylindrical to rectangular ... (for unit vectors)

lol ...

There's a solution for the problem ... and the writer gives strange solution .... (for the question Gradient is invarient to coordinate transform)

He uses $ e_1 = a_{11} l_1 + a_{12} l_2 + a_{13} l_3 $ ... $ e_1 $ and $ l_1 , l_2, l_3 $ being unit vectos

same is the transformation rule for coordinate systems

user19161

10:31

@anon For one, I don't employ sarcasm.

experimentX

Though ... if i replace coordinates by unit vectors, and divide by madnitude of Jacobian ... i seem to get transformation relation between unit vectors

would it be a good question if I post??

J. M.

@robjohn Ooh, neat answer. :)

experimentX

Question goes like this

Let the transformation rule between two coordinate systems $ (x_1, x_2, x_3) $, and $ (u_1, u_2, u_3) $ be
$$ x_1 = a_{11} u_1 + a_{12} u_2 + a_{13} u_3 \\
x_2 = a_{21} u_1 + a_{22} u_2 + a_{23} u_3 \\
x_3 = a_{31} u_1 + a_{32} u_2 + a_{33} u_3 \\ $$

If $ \hat e_{x1}, \hat e_{x2}, \hat e_{x3}$ be the unit vectors in $ (x_1, x_2, x_3) $ and $ \hat e_{u1}, \hat e_{u2}, \hat e_{u3}$ be the unit vectors in $ (u_1, u_2, u_3) $, What would be the transformation relation between unit vectors (both from $ \hat e_{x1}, \hat e_{x2}, \hat e_{x3}$ to $ \hat e_{u1}, \hat e_{u2}, \hat e_{u3}$ and vice v…

Rajesh D

I have quick question. Something splashed in my mind, and i'd like to know whether it makes sense, if so references and some trivia and facts about it. We know that the convolution of a function with a mollifier (or any smooth function) is always smooth. What about convolving a smooth function with a distribution (for eg. a combination of dirac deltas) Can the resultant function be non smooth? Where are these kind of things delt with

experimentX

does it make any sense??

Frank Science

10:38

What about my problem math.stackexchange.com/questions/158232/…

0

Q: Equation about generating functions and subfactorial

Suppose $G_n(w)$ is a formal power series, try to solve out $G_n(w)$ for all $n\ge0$ from the equation: $$\sum_{n\ge0}z^nG_n(w)=we^z\sum_{n\ge0}\frac{!n}{n!}z^nG_n(w)+1-w\tag1$$ where $!n$ is $n$-subfactorial which satisifies $$\frac{!n}{n!}=\sum_{k=0}^n\frac{(-1)^k}{k!}$$ Any help? Thanks! Th...

experimentX

I hope it makes sense

0

Q: transformation of unit vectors between coordinate systems

Let the transformation rule between two coordinate systems $ (x_1, x_2, x_3) $, and $ (u_1, u_2, u_3) $ be $$ x_1 = a_{11} u_1 + a_{12} u_2 + a_{13} u_3 \\ x_2 = a_{21} u_1 + a_{22} u_2 + a_{23} u_3 \\ x_3 = a_{31} u_1 + a_{32} u_2 + a_{33} u_3 \\ $$ If $ \hat e_{x1}, \hat e_{x2}, \hat e_{x3}$ ...

transformation

robjohn

@JM Thanks. There are precious few inversive-geometry questions :-)

J. M.

@FrankScience You've tried Cauchy's differentiation formula?

J. M.

11:00

Heh.

Frank Science

11:14

@JM What?

J. M.

@FrankScience You're essentially looking for a general expression for the derivative of your GF, no? Cauchy can help with that.

Frank Science

@JM Solving it, not only for the derivative.

@JM Is my title inexact?

@JM The contents after the horizontal line only explains something I've got.

Eugene

@robjohn sorry to hear that. I hope she get better soon.

robjohn

@Eugene Thanks. I don't know when she is going in for the pacemaker.

Eugene

@robjohn nothing scheduled yet?

Frank Science

11:19

@Eugene Is somebody ill?

robjohn

@Eugene Nope. My wife is heading there again tomorrow.

Eugene

@robjohn i see. i really hope all goes well.

robjohn

@Eugene actually, it is already tomorrow :-) make that later today.

@Eugene thanks!

Eugene

@robjohn she has insurance right?

Frank Science

How to treat a generating function equation?

Supposing that $G(z)=\sum_{n\ge0}a_nz^n$, how to denote $\sum_{n\ge0}\frac{!n}{n!}a_nz^n$?

NinjaTurtle

12:44

Hey @Gigili You changed you profile pic?

Gigili

Did I?

NinjaTurtle

Ask yourself :)

Gigili

asks herself: did you change your avatar?

NinjaTurtle

What answer did you get?

What are you looking for? Go away.

Gigili

Hey, I have a strong sense of deja vu.

Where have I seen that sentence and that avatar?

That's odd.

NinjaTurtle

12:48

Which one?

Earlier one was better :)

Gigili

> What are you looking for? Go away.

NinjaTurtle

Both were cool.

Benjamin Lim

13:15

@robjohn I am very confused here: math.stackexchange.com/questions/158575/… Do you think you could provide an answer here?

Matt N.

13:36

@BenjaminLim Hi there. Thanks for your answer.

I was enjoying myself so far (reading AM). And then this chapter about extensions and contractions in rings of fractions seemed so unbearably boring.

Nearly bored myself to tears.

@BenjaminLim Have you already finished reading AM?

bbl

Zhen Lin

sigh More abuse of MathJax for text formatting...

J. M.

@ZhenLin Oi. Where is this?

Zhen Lin

Benjamin's question.

J. M.

*facepalm*

robjohn

14:24

@ZhenLin The chain-rule question?

Zhen Lin

I guess?

robjohn

@ZhenLin this one?

Zhen Lin

Yes.

Frank Science

14:42

I'll enter college and study math. Any suggested books? for real analysis or something else

Analysis

Or calculus?

Ragib Zaman

Study some linear algebra and group theory.

College will take care of analysis for you just fine.

@FrankScience I forgot to tag you.

Jordan

14:58

Hey gang

Frank Science

@RagibZaman But Concrete Mathematics appears many details about analysis, for example, series.

Ragib Zaman

@Jordan Hello

Jordan

I am trying to do a differential equation and I am confused about something. I have $y' + 2y = 2e^x$ I can't really take the integral of the left side though because I need it to be multiplied by dy not added right?

Frank Science

@RagibZaman although the 2nd chapter defines infinite sums in a different way, the succeeding chapters also uses series.

Ragib Zaman

@Frank I know, but that's exactly the trap you can't fall into (it's what happened to me!). You will encounter analysis a lot in books you are more inclined to read because it had things you have at least a small amount of familiarity with, because most people take calculus before group theory or linear algebra. You will see analysis pop up lots, so actively study algebra at least for now, colleges stress calculus/analysis in the first 1.5 years so that'll come on its own.

Frank Science

15:01

Now I'll advertise my problem here. math.stackexchange.com/q/158232/23875

Gigili

@Jordan Huh? Why can't you?

Frank Science

@RagibZaman Before that, how can I understand stuff in CMath or taocp?

Jordan

Because I need $2y dy$ for an integral don't I?

Ragib Zaman

@Frank is CMath Concrete Mathematics? and what is taocp?

Frank Science

@RagibZaman Yes, and taocp == The Art of Computer Programming

Ragib Zaman

15:04

@Frank I don't think either of them actually needs much "analysis" though perhaps a college level calculus class would be needed.

Gigili

No, it would be $y+y^2=2ye^x$

That is, you have $\int (y' + 2y) dy = \int 2e^x dy$

Ragib Zaman

@Gigili I dont understand...

Frank Science

@Ragib What's the analysis more than calculus?

Ragib Zaman

@Gigili y is a function of x so the integration doesn't work out how you say it does.

Frank Science

@Ragib Tak some countexample(I can't spell well)

Gigili

15:06

@RagibZaman It does.

Jordan

I start with $\frac{dy}{dx} + 2y = 2e^x$

Ragib Zaman

$\int 2e^x dy \neq 2y e^x$

@Frank Analysis goes FAR beyond calculus!

Frank Science

@Ragib examples please.

Ragib Zaman

What do you mean by an "example"

Frank Science

@Ragib What's beyond

Ragib Zaman

15:08

I can list fields of analysis that are not calculus?

Gigili

@RagibZaman You better focus on one problem at a time.

Frank Science

@Ragib not enumerate, only an example

Gigili

@Jordan And what do you want to do?

Ragib Zaman

@Gigili I have one discussion and one mathematical problem, I can handle both.

Gigili

I'm not sure.

Ragib Zaman

15:09

@Frank Ok, the theory of functional analysis is considered analysis yet is far departed from what you would call calculus.

@Gigili please explain to me then how you conclude that $\int 2e^x dy = 2ye^x$, even though $y$ is a function of $x$ ?

Frank Science

@ragib sorry, I have meant that the course named after mathematical analysis or real analysis, not functional analysis.

Jordan

@Gigili I need to solve for y

Ragib Zaman

@Frank I don't understand, Functional analysis is a subfield of mathematical analysis?

Frank Science

@ragib I don't know the distribution of courses in your country. What will a math course student first learn about analysis?

Ragib Zaman

@Jordan You have to solve $y'+2y = e^x.$ That $=e^x$ makes the problem quite hard. Do you know how to solve the simpler problem $y'+2y = 0$ ?

Frank Science

15:12

@ragib a university student who work on math. sorry for my bad english

Jordan

No there isnt really a good example in my book, they all use things like $y' = 2y^2$ which I can do

Ragib Zaman

@Frank Well, Calculus can be considered the roots of analysis, so you learn about derivatives, integrals, the mean value theorem, taylor series, that sort of stuff. Have you seen those before?

Frank Science

@Ragib I know, but lack a system studying.

Gigili

@Jordan Well, write it as $\frac{dy}{dx} = 2e^x -2y$ Then take the integral

Jordan

How can I take the integral with x and y?

Ragib Zaman

15:15

@Jordan I think you should listen to me for a while, Gigili seems to be a little confused at the moment.

Frank Science

For example, $\varepsilon$-$\delta$.

Ragib Zaman

@Jordan Okay lets try to solve y'=y. Do you know what the solution to that is? Try to think of a function you've seen before that does that.

Gigili

Listen to that guy for a while, he's in urgent need of attention.

Ragib Zaman

@Frank Ahh well that's more college level calculus/analysis, not usually taught in high schools. In some calculus courses you may see some basic "real analysis" like epsilon delta definitions of limits, sequences, series, convergence

Eugene

hi all

Ragib Zaman

15:17

@Eugene Hi

Jordan

actually I think this problem is more simple than I thought

I am also given what y is equal to in terms of x so I think I can just integrate that and put that in place of y'

Gigili

@Jordan Nonono, follow his step-by-step guide and it'll be solved by tomorrow morning.

Jordan

:(

Ragib Zaman

@Gigili I don't understand what you are implying. If Jordan listens to me I think we can get it done without fuss reasonably quickly.

Eugene

well i'm off now. bye all!

Ragib Zaman

15:20

@Jordan What did they book tell you $y$ was equal to in terms of $x$?

Gigili

@RagibZaman I told him to listen to you, I don't know what else I can do.

Jordan

Show that $ y = \frac{2}{3} e^x + e^{-2x}$ is a solution of the differnetial equation $y' + 2y = 2e^x$ I think I can solve it now

Gigili

Don't listen to me, Jordan. Don't listen to me.

Ragib Zaman

@Gigili I was not trying to offend you, I am sorry if I did.

Jordan

Oh wow I think I got anon suspended

Ragib Zaman

15:21

@Jordan Good. Next time you should tell us the entire question, it will help us help you better.

@Jordan It wasn't you that got anon suspended, just an over-reactive moderator.

It was only a 30 minute suspension anyway, I think everyone is over it.

Rajesh D

hi folks

skullpatrol

hi

@DylanMoreland hi

J. M.

Mistakes happen. We move on from 'em.

skullpatrol

Sometimes we even learn from them ;-)

Frank Science

@RagibZaman what about Сборник задач и упражнений по математическому анализу

@RagibZaman By Soviet mathematician Boris_Demidovich

Ragib Zaman

15:38

@Frank Sorry, I have never encountered that book before.

Frank Science

@Ragib How many exercises are neccessary?

amazon.com/Problems-mathematical-analysis-B-Demidovich/dp/…

Ragib Zaman

I would recommend an instructional text more than a problems text, instructional texts will contain more than enough problems for you.

Frank Science

15:56

1

Q: Equation about generating functions and subfactorial

Suppose $G_n(w)$ is a formal power series, try to solve out $G_n(w)$ for all $n\ge0$ from the equation: $$\sum_{n\ge0}z^nG_n(w)=we^z\sum_{n\ge0}\frac{!n}{n!}z^nG_n(w)+1-w\tag1$$ where $!n$ is $n$-subfactorial which satisifies $$\frac{!n}{n!}=\sum_{k=0}^n\frac{(-1)^k}{k!}$$ Any help? Thanks! Th...

power-series generating-functions functional-equations

Bill Dubuque

@MattN Because the rest of Atiyah-Macdonald will exploit to the hilt the local-global approach, it is essential to know by heart those properties of localizations.

robjohn

@FrankScience Please read the Chat Rules, in particular.

Frank Science

@robjohn sorry.

robjohn

@FrankScience It's okay. People usually find it spammy to see things over and over.

Frank Science

@robjohn okay.

robjohn

16:10

@JM after we slip on them and fall on our... :-)

Ragib Zaman

I think I witnessed a case of cyber-bullying earlier.

robjohn

@RagibZaman when was that? or where?

Ragib Zaman

About an hour and 12 minutes ago.

J. M.

@RagibZaman On Jordan?

Ragib Zaman

Yes.

I can't be certain, but I think Gigili knew the statements he was making we're incorrect.

To intentionally lead a student astray when they are confused as it is and trying to learn...I don't like that.

Frank Science

16:14

What's cyber-bullying?

J. M.

*sigh* it's become a vicious cycle, last I checked. He rails about how helpless he is and how the people here make him uncomfortable, others attack, and thus his beliefs are neatly perpetuated. Yeesh.

@FrankScience You at least know what "bullying" is, no?

Frank Science

@JM wikipedia en.wikipedia.org/wiki/Cyberbullying tells that it's an illegal thing?

J. M.

@FrankScience Well, these Americans are a litigious society...

Here we just stick up for people who get trampled on.

robjohn

@JM I take offense at that. Expect to be contacted by my lawyer! :-)

J. M.

See? :)

robjohn

16:17

@JM I see what you mean! :-)

J. M.

(My opinions on lawyers, on the other hand, are for another time and place.)

robjohn

@JM be careful... my wife is a lawyer :-p

J. M.

But getting back to your client, Ragib: it was nice that you were patient with him.

@robjohn Another time and place. ;) (Also, generalities almost always have exceptions.)

Ragib Zaman

I expect better from members of math.se than to try to implant incorrect mathematical ideas into struggling students. I consider it far more dangerous than, say, anon's chat comment that got him suspended.

J. M.

I still can't wrap my head around what was suspension-worthy about that bit. anon actually took it back within the span of a minute or so, and even then, it was more an observation than anything.

But hell, people can be nuts. Even mods.

Ragib Zaman

16:21

It was the mildest of insults, I think Jordan has thicker skin than that.

robjohn

@RagibZaman There are always extremes to any group. I think that the mixture of two extremes may exhibit some situations that are not typical.

I am not making an excuse for the situation that you mention, just don't judge on that occurrence.

Matt N.

@BillDubuque Right, thanks.

Hello everyone.

robjohn

@MattN hey there :-)

Ragib Zaman

Well, it would seem unfair that anon gets suspended for his mildly insulting observation yet Gigili experiences no consequences for trying to implant incorrect ideas into a struggling student.

5

It could potentially have put into doubt many hard hours by Jordan and math.se members into understanding such concepts.

Matt N.

@robjohn I'm not sure how to cope with the stress induced by 2 exams and a BSc's thesis : (

I feel like I'm about to hang myself.

J. M.

16:23

@MattN No breaks for you?

Matt N.

Although I don't have the guts to do that.

robjohn

@RagibZaman I do find the reaction against anon to be very odd. I have felt similar things (but bitten my tongue, or fingers).

J. M.

@MattN On that subject: using a rubber band for the hanging is a bad idea. You get a few concussions along with the usual...

Matt N.

@JM Not really. Although I am going away for ten days on Sunday. But in retrospect, that wasn't such a good idea. But I haven't had any holiday in 3 years and I've been feeling dead for quite a while now. So last month I decided that these 10 days were a good idea.

robjohn

@MattN rope is less messy, but don't do it in any case...

Matt N.

16:25

@JM Bungee jumping? No thank you.

J. M.

@MattN Yeah, I was trying to lighten your mood with an old joke. :)

robjohn

@MattN Just yesterday, I got this in a fortune cookie: The problems of today will soon be buried by the sands of time.

Matt N.

@JM : )

J. M.

@robjohn and then poked upon by future archaeologists...

Matt N.

@robjohn Wise dat. OTOH, it's still today. : )

robjohn

16:28

@MattN and soon it will be tomorrow.

Matt N.

No, seriously. This is a very uncool situation.

But carry on, I didn't mean to kill the conversation that was going on when I entered the room.

J. M.

@MattN Don't fret too much, it'll pass. Besides, you've got people you can ask help from if need be, right?

Matt N.

@JM By that you mean I've got SE?

Yes, that's right.

My life was pretty miserable before SE. : )

You are all awesome.

I wonder how I even managed a day without you before SE... scratches head

Wot? @anon got banned?

anon

@FrankScience Rendering off and rendering on refers to editing questions on the mainsite, not the chatroom.

Indeed.

Matt N.

Who did you "offend"?

Frank Science

16:36

@anon What do you mean by "rendering"

anon

dude, there's a screenshot linked in the starred comment @MattN

Matt N.

@anon Oh, didn't see that, sorry, was reading the transcript.

skullpatrol

We are the world ...

anon

@FrankScience When the rendering is on you will see LaTeX equations in the preview. When the rendering is off you will only see raw LaTeX code within dollar signs.

Matt N.

That's not even mildly offending. Seems unjust that you should get banned for that.

Frank Science

16:38

@anon But it seems no effects, when I use the javascript for rendering off.

anon

@FrankScience Go on the mainsite, type some stuff in somewhere, then click rendering off, then type something in the textbox. If it doesn't turn into raw code in the preview then either you're doing something wrong or it works different in firefox than chrome or you'll have to ask robjohn (it's his script).

Frank Science

@anon It's for tomorrow.

J. M.

@MattN Eh it's nuts. If it happens again, we revolt.

Matt N.

@JM Yep.

Sorry, to link to this but which "Paul" is he talking about?

anon

Paul's Online Notes

Matt N.

16:44

Good. I was going to flag his comment if he'd been complaining about Paul Slevin.

anon

He asked his question on the mainsite (with a follow-up on rectangles).

Matt N.

He should stop hating and use the time for thinking.

J. M.

If there is at least one thread on meta dedicated to your behavior, you should probably re-examine how you're dealing with the site and its members...

Frank Science

@anon Why -4?

anon

Someone did flag one of his comments about hating Paul or Stewart or hoping one of them was in misery, but I was unsuspended by that point and invalidated it. He was just venting with no one around.

Matt N.

16:46

@MB +1 for your profile. I fancy topology, too : )

anon

@FrankScience The first one or three probably because of "that horrendous site." That last three or one because of that and the first downvotes...

Frank Science

@anon The link has maleware?

anon

Also there are a nontrivial number of people that don't like Jordan.

M.B.

@MattN :)

Matt N.

@anon Makes me feel a bit sorry. If I make it through my own "situation" I'll help him with his problems after mid-September.

J. M.

16:47

@FrankScience No, he was just venting.

anon

@FrankScience No, his comment about "that horrible site" (direct quote) from the first sentence in the post.

Matt N.

If I fail my exams or thesis OTOH, I might consider getting myself some rope.

Frank Science

But his problem is objective, not attacking someone?

anon

Which people would disagree with or at least dislike Jordan's attitude over.

J. M.

When doesn't incessant whining not rub people wrongly?

Matt N.

16:49

@FrankScience No. His opinion about Paul's online notes is quite subjective, imho.

Frank Science

Oh, I see.

It's too late, I'll sleep

Matt N.

@JM Oops. True dat. I better stop now and pull myself together.

@FrankScience Good night.

J. M.

@MattN Let's keep our fingers crossed. For now, stay away from cordage...

skullpatrol

@anon Are you among that nontrivial number now?

Matt N.

@JM Yes.

anon

16:50

Mixed feelings, but I don't just downvote people I don't like.

J. M.

@MattN Eh, at least you don't have learned helplessness.

Frank Science

But I think downvote is not good. It's necessary for somebody to edit his post, removing the subjective words.

J. M.

@FrankScience That would have been the best course of action, yes.

Frank Science

downvote is good enough.

I cannot explain what I mean.

J. M.

@anon Mixed feelings - what you feel when you see your worst enemy driving off a cliff in your brand new Ferrari.

Matt N.

16:52

: D

@JM Actually, no. Assuming you can always replace your car with a new one.

Hey @anon do you know a bit about quadratic forms?

(or anyone else in here)

J. M.

If you're rich, I suppose, but losing a Ferrari is still painful.

anon

Not much.

Matt N.

Ok.

Frank Science

I mean that we should do something, not only downvoting.

anon

But you might as well just ask, Matt..

J. M.

16:54

@MattN what about?

Matt N.

@JM I guess I can't relate to the feeling of loss because I wouldn't want a Ferrari even if I could afford one : )

J. M.

@MattN Damn, I guess you're not part of that gag's intended audience...

Matt N.

Ok, gimme a minute to formulate the question.

M.B.

@MattN: well, most of the oral exams in my department are held at floor 7 or higher so the precautious examiners close the windows prior to announcing the results ;) (Not really, but someone (supposedly) jumped from the 13th floor in the 80's.)

anon

@FrankScience The four downvotes were all before I even looked at the question, so it's likely they will not come off (users that downvote quickly are not highly correlated with users that check old downvotes to see if they should be removed..), but if you edit out the comment it will bump the question and I suppose some will upvote it then. But I don't take responsibility for that.

Matt N.

16:55

@MB OTOH, I can relate to that : )

anon

Then again someone may just see the four downvotes and the OPs name and downvote again ...

J. M.

@MB Very prudent.

@anon Ah, voting patterns...

anon

It's only just dawned on me that people use "basis" when technically they mean ordered basis.

Ragib Zaman

@anon What do you mean exactly?

anon

You mean with my basis comment?

Ragib Zaman

17:02

yea

anon

take for example this answer

Matt N.

So I have Ernst Witt's complete collection of works in front of me. And the first paper is about quadratic forms on arbitrary fields. He says that Minkowski had studied quadratic forms over Q.
But I don't know why we even want to know when one quadratic form can be transformed into another. Geometrically, that is.

So, I don't really know anything about this, but I think we can define a bilinear function on a simplectic vector space. And we can make this bilinear function a quadratic form.

anon

@RagibZaman In order to get an isomorphism $V\cong F^n$ using a basis for $V$, you need to know where to send each basis vector, but there are $n!$ choices unless you have an ordered basis, in which case there's a distinguished map sending the first to e1 etc.

Ragib Zaman

@anon Ahh I see. I guess that's just so ingrained in how we normally see/use a basis that we forget it's even something to mention.

anon

@MattN In every field?

Frank Science

17:05

@anon But I think something instructive is far more important than the reputation of someone. We should keep educating.

Matt N.

@anon The title of the paper is (translated from German): "Theory of quadratic forms on arbitrary fields".

anon

@MattN I was responding yo your comment that every quadratic form can be transformed into another, quadratically.

You can't transform $x^2-y^2$ into $x^2+y^2$ in the reals for example.

Matt N.

@anon Ah no, that's not what I meant. I meant that some quadratic forms can be transformed into others and we want to study when one can be transformed into another.

But it's not clear to me why we'd want to know that. What information do we get if we know we can "transform" one into another?

Eugene

@MattN have you read the wiki page on quadratic forms? it seems to mention what you're asking

anon

@MattN It just means two quadratic forms are "the same" up to basis, no?

Matt N.

17:09

@anon Yes, it probably does. But what does it tell us?

What do we want to do with this information?

Eugene

the wiki page has a section on "geometric meaning"

anon

@MattN Maybe they have the same invariants (up to something), or induce the same geometry, or maybe it's useful for classification of quadratic forms, I'm not exactly sure.

Maybe it's just nice in and of itself to know when two objects are the same up to some isomorphism.

J. M.

Or on a geometric tack: it's nice to know if one ellipse (or some other conic) is just a shifted/rotated/reflected version of another...

Eugene

@JM indeed.

or if it is the same as a paraboloid even by some transformation

in algebraic geometry it is useful to find representations at a point $P$ such that the form is nonsingular as well.

J. M.

Segue: we have six people with "Tenacious" now. If we get an "Unsung Hero", then math.SE is officially crowded.

Eugene

17:16

@JM i once saw that badge and wondered how it would be possible to get it

i thought that the only way would be to create multiples

anon

Wow, didn't expect Mitra, Lim or Taylor on that list.

J. M.

@Eugene That would happen if the only people who paid attention to your wonderful answers was the OP of the questions you answered, and even they didn't bother to upvote.

Eugene

@anon i'm surprised david loeffler asked a question on MSE before.

Ragib Zaman

I think most of those people just got the badge very early on when they had only a few answers.

Eugene

@JM usually the OP would upvote you though no?

J. M.

17:18

@Eugene Usually. Unless OP's unregistered, for instance.

anon

@RagibZaman Oh yeah, I forgot that badges are permanent so that makes sense.

Ragib Zaman

For example Ben Lim only has 7 accepted answers with 0 upvotes, not a huge amount. He has a total of 187 answers.

Eugene

@JM true. 10 unregistereds required though

experimentX

Hi ... can anyone help me with this question?? just a hint would be lot helpful

1

Q: transformation of unit vectors between coordinate systems

Let the transformation rule between two coordinate systems $ (x_1, x_2, x_3) $, and $ (u_1, u_2, u_3) $ be $$ x_1 = a_{11} u_1 + a_{12} u_2 + a_{13} u_3 \\ x_2 = a_{21} u_1 + a_{22} u_2 + a_{23} u_3 \\ x_3 = a_{31} u_1 + a_{32} u_2 + a_{33} u_3 \\ $$ If $ \hat e_{x1}, \hat e_{x2}, \hat e_{x3}$ ...

transformation

Eugene

anyway i'm going to learn some analytic NT now.

bye all

anon

17:23

@experimentX that's just linear algebra

experimentX

yes .. but i had difficulty with inverse ... from cylindrical to cartesian

anon

cylindrical??

That's a linear coordinate transformation bro, it only takes cartesian to cartesian.

experimentX

Hmm ... isn't there going to be general transformation system between coordinates systems??

anon

Yes, $\vec{x}=\vec{F}(\,\vec{u})$, much more complicated

ie $x_1=f_1(u_1,u_2,u_3), x_2=f_2(u_1,u_2,u_3), x_3=f_3(u_1,u_2,u_3)$, with some regularity conditions (like nonsingular Jacobian determinant of $\vec{F}$) stipulated on the functions

experimentX

Oh ... if you can some time ... can you answer that question ... I have lot of confusion ...

anon

17:32

I'll answer your question on the main, but it won't touch any trouble you may have transporting between cartesian and cylindrical coordinates (you'll have to clarify that question separately)

experimentX

Okay ... sure

Gigili

@RagibZaman You can stop talking about me, I know what to do and am not interested to hear anything from you.

I'm sick of flagging messages and fights, otherwise I'd definitely flag that message of yours.

Leave me alone.

Ragib Zaman

@Gigili Please flag any messages of mine you found to be inappropriate. I will not confront you for doing so, it is within your rights. I don't want to fight either.

Gigili

17:48

Well, I leave the place for you and all the stupid people who think I was misleading Jordan intentionally. I made a mild mistake there because I wanted to answer his questions immediately. I am a human being after all. I thought people knew me better. (I don't care about you at all, I mean other users that I spent time with)

experimentX

thanks @anon you are a lifesaver .... can you tell me one more thing?? is determinant of that matrix going to be unity??

anon

Not necessarily. The determinant can be any nonzero real.

@experimentX Also, sometimes people will write something in cylindrical coordinates as $ae_r+be_\theta+ce_z$ or something like that. It's a bit of an abuse because it is not Cartesian.

experimentX

Hmm ...

anon

The transformation rules in that case would be $ae_r+be_\theta+ce_z$ being the same as $(a\cos b,a\sin b,c)$ in Cartesian coordinates, which you can see on the Wikipedia page for the cylindrical coordinate system (with whatever letters people choose to use)

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