@Chris Yes that's correct.

In fact if you put [[7+a,2,3,3+a],[2,7,7,11],[3,7,7,2],[3+a,12,2,11]] you will find out that there is only one value of a for which determinant is non-zero, i.e. only one value of a for which the rank is lower than 4.

wolframalpha

Yes I've thought of that way but I wasn't sure how to put it in the answer :-/ (I mean formally) Can you think of a way?

wolframalpha

You just use the result thank rank(A)=n (for square nxn matrix) $\Leftrightarrow$ A is regular $\Leftrightarrow$ determinant of A is non-zero.

Both are well-known characterizations of regular matrices.

OK then, thank you @MartinSleziak

@Martin: may I ask a question?

ok @Ilya.

I'll have to go afk in 10-20 minutes, but if I do not know the answer, perhaps someone else here will do.

@MartinSleziak that's about Lemmas, Theorems and Propositions. I agree with Matt here - but I have some doubts if it is OK to use in one paper Lemmas, Theorem, Propositions, Corollaries and Remarks

Just wondered what is your impression

That answer seems very reasonable.

I would use proposition for anything which does not go along the lines of the main interest of the paper, but is worth pointing out. (Might be for interest for others.)

it is reasonable, but since I'm writing a paper (~30 pages 1 column) rather than a book, I wonder if it is too much to use all 5 types

I don't prove remarks, though :)

It is certainly ok to use all of them in the same paper - at least many papers have all of them.

ok, thank you :)

Some people have even environments for Examples.

But they appear probably more often in books.

oh

I use them also - I write papers with the use of measure theory for CS guys, so I think it is worth enlightening results with Examples

not to mention the final case study

ok, I'll have to go

good luck :)

bye

hey

no one around?

@ClarkKent hey

@ClarkKent there is one guy asking about a lot of topology quesitons

@Chris any matrix is already a linear map

No

@Chris What's the definition of a linear map?

yes

so if a matrix has not its full rank, shouldn't it be a problem somehow?

no

@Chris only for inverting it.

how has rank got to do with the map being linear?

@Chris Not having full rank means that it does not reach all of its range space, and so there are some elements that can't be mapped to, so the inverse for those elements can not be defined.

@Chris said simply, the rank of a matrix has nothing to do with a matrix being a linear map or not. en.wikipedia.org/wiki/Linear_map#Matrices

@Chris In what way would mapping to a proper subspace keep a map from being linear?

ok

Hi folks!

I have a question for you guys. not sure if this is the right place or not.

I have a very heavy object (car frame) that I want to weigh. I can't get the entire thing on the scale all at once. is there a way to calculate total weight by weighing each end?

@dave : no idea how to do it, one idea i get is to have two or more weighing machines and use them simultaneously placed symmetrically underneath it

@davethieben If both ends are at the same height and you support and weigh at the same points, then just add the weights

They do not have to be placed symmetrically underneath it.

@Mark : atleast to avoid overloading of any of them. What say

Sure. But as long as no scale's upper limit is exceeded, the sum will be the same regardless of whether all the scales show the same weight.

I agree

On the other hand, weighing each end separately is a very tricky matter, because to weigh only one end, you have to be holding the other end, and you can't be sure you will do it the same way each time.

@MarkDominus yes. If you weigh it all at once on several scales, then just add the weights.

yes a bit of mechanics is needed

A classic strategy is to load the heavy thing onto a boat, and then mark the lowered waterline on the side of the boat. Then take the heavy thing off and load the boat with smaller weights until it sinks the same amount; then weigh the smaller weights separately and add them up.

@MarkDominus Then to find out if the frame is made of gold...

@dave : too much to ask, can you upload a photo of it?

well if I weigh one end, the other end will be resting on the ground

That's no good.

yes but at what angle ?

it would be nearly 0.

then create same situation for the other end, then yopu may need some simple calculations

@davethieben then back to my previous comments about weighing and supporting at the same points and keeping those points at the same height

so, assuming the object is not inclined at any observable angle, the weight at one end will be half the weight of the object?

Only if it is symmetric.

The thing seems very dicey to me.

I guess I'll have to find another scale

If the mass is unevenly distributed...

What if you rig up a long lever that you can use to lift it completely off the ground? Then you can measure the force you use to lift it up,and the length of the lever and calculate the weight from that.

@MarkDominus That works, but building the lever for the sole purpose of weighing the car seems like a lot of work that he could instead expend on finding a nice scale...

Or maybe he already has a block-and-tackle lifting device in his engine yard.

The same principle works there. As long as you can get the whole thing off the ground at once.

yeah, it's about 15 feet long and probably weighs 300 lbs. I'd need a hell of a lever.

keeping aside the objective of getting an accurate weight, What is your actual purpose?

just want the weight. doesn't have to be extremely accurate... +/- 5lbs would be fine

I'm trying to weigh everything that goes into the car

I have another idea! Advertise in the local paper that you have a 900-pound piece of scrap metal for sale cheap, at a per-pound price, to anyone who will come take it away. If someone comes by to buy it, they will have to weigh it themselves to make sure you are not cheating them. If they come back later and say "You thief, that frame weighed only 637 pounds!" then you have your answer.

bahahaha

genius!

including the likes of engine and stuff, I thought you just wanted the weight of the frame which could be obtained from the geometry of the structure and the density of the material

@MarkDominus I'm a fan of subterfuge... :)

I could load it onto a trailer and go to the public scales, but I dont have a trailer handy

@davethieben You can't rent one?

Hacking up a lever would be cheaper.

@JM I could, but it's not really worth it

Don't you have a block-and-tackle thing for pulling engines out of cars?

@dave : I have a brilliant idea, if you don't mind cutting it into pieces and dismantling!

lol

lol

@MarkDominus no. I can borrow an engine hoist.

Now I'm not convinced this will work. Also it depends a lot on the details of the engine hoist.

thanks for the ideas. I think weighing each end and/or finding another scale will work well enough.

Hi @JM

Hello

does anyone have some good recommendations for an introductory differential equations book?

one with good explanations and LOTS Of exercises?

Hi; any mods around?

hello, I have question guys, I answered a question on MSE and I know it clearly is wrong , but i cannot seem to find any mistakes, here is the link to the answer math.stackexchange.com/a/144997/21832 , i cant seem to understand how does indefinite integration and definite integration yeild different answers, and any advice on what i should do? i have 3 choices, to delete the question, andd community wiki to it, or put it up as another question,

ok i added community wiki to it,

@MarkDominus But then they might have already cut it into pieces 8-)!

hey i'm trying to understand my anova data would anyone be willing to help out?

@caseyr547 Umm, what is it?

Okay, nice.

@Gigili i am doing one way anova and multiway anova and the answers dont match...the mutliway anova give a tiny p value to a column that doesnt corrolate well with the test data. i have posted my question here stats.stackexchange.com/questions/28542/… and here stats.stackexchange.com/questions/28537/… thanks

It has been a quiet morning. The conversation regarding weighing of car frames has not even scrolled off the screen.

@SauravTomar You wrote "and since variable dont matter in integration". That is true for definite integration where the limits track the change of variables. For indefinite integration, the variable of integration is exported to the outside world. You cannot just change variables back to a variable you've used before.

@SauravTomar As you have probably seen, I have commented on your answer. If you don't understand what I wrote, we can discuss it here.

@tb here you go :-) i.sstatic.net/fSKja.png

Where's Tee-Bee?

@Gigili He's not here right now, can I take a message? :-D

Hih. Tell him that I miss him.

Hey anyone around want to help me with some relatively simple trig? I have a formula written i just need to re-calculate some values given a new coordinate plane

it involves a baseball field and angles

@matt: What's the problem?

let me upload the plane that im trying to plot against and describe the problem a little better

1sec

we receive a y coord (letter designation C-X) and then an x coordinate (0-425ish)

im trying to recreate a formula to take those coordinates, and give me a 'left' and 'bottom' value in pixels to render a dot over the landing spot of the ball

i wrote it once with some help from someone here but i forgot to save the convo so i dont know how to recalculate the values for this new plane (the proportions and dimensions have changed a bit)

i can dig up the old plane that the original formula was based on if that would be helpful

er sorry the x-coord is C-X, y coord is 0-425

@mattacular: Don't worry about it - here is a link to your conversatino with Henning where you did this

oh wow

even better!

he was extremely helpful i wanted to thank him again

thanks a lot for helping me find that though, i will be able to recreate it based on that

i think :)

@mattacular I calculate about 4.8° per letter

thanks rob!

Is that what you got before?

the proportions changed drastically since the first time we did it but let me check

the first angle function was ((letterIndex - 13.5)*pi/42)

so C letterIndex = 3

D = 4 etc

That looks like about 4.3° per letter.

that sounds right

it got squeezed basically

I was just going from the image posted.

i was about to check if that angle func is still viable or not it may be

@caseyr547 Oh, well.

It's, um, a bit complicated.

@robjohn actually the old angle formula still seems fine i just need to tweak other parts of the equation

its slightly off but this doesnt need to be 100% accurate just close enough

which is -

left: absoluteValue(Math.sin([ANGLE]) * distance * 0.50)

distance being the y-coord

bottom: absoluteValue(Math.cos([ANGLE]) * distance * 0.50)

that might not make any sense to you though :)

No, that makes perfect sense. It has to be of that form.

so it actually looks pretty accurate with all those values

the angle is just a tad off but not a big deal IMHO

really?

i dont have that much karma or whatever :/

thanks though

@robjohn So, are Bezout jokes allowed once you're a mod? (no more trashy ones of course)

ok thanks very much robjohn, mixedmath for all the help! you all rock

@ClarkKent Use your superpowers, which, here, better include ultrapowers!

Over here, the law of excluded middle is a superpower...

@ZhenLin Huh, active construction?

Something like that, I suppose.

@ZhenLin Does "here" refer to chat or where you are?

Hmmm... yes, I suppose it's true that the law of excluded middle is regarded with a little suspicion in my research group.

My top three candidates are in order from left to right on the chat activity section -->

@ZhenLin Ah, I see, so there goes my appeal to ultrapowers.

I quote from a past exam paper, "If you wish, you may assume classical logic when answering this question, but full credit will be given only for constructively valid answers."

@ZhenLin Wow. What school of constructivism are you in?

Nah, I'm half-joking. That was from a course by P.T. Johnstone ten years ago, "Constructive Topology".

@ZhenLin I've enjoyed reading some of his work. Are his lectures as engaing as his writings?

Hmmm. His lectures are certainly clear and concise... so much so that I failed to appreciate it as a first-year undergraduate. But I found his Algebraic Topology course very good when I was a third-year.

@BillDubuque Oh, I just noticed the elections are closed. Have the results been posted?

They closed like 30s ago.

Just some initial stats

@robjohn Speech, speech!

(is all I can see...)

@TheChaz where?

At the election page

I see Download the election data but no tabulation of results.

394 voted? Only? Pah.

I was surprised by the vote rate at first, but then remembered that the front page is mostly <200 users

And we tend to get a lot of hit-it-and-quit-its around here...

I guess I could tabulate them myself, but eh.

about elections

@MarkDominus Oh?

Oh what?

You could?

Sure, that's why the data is available for download.

Umm.

Hm, I thought Akhil Mathew was a mod here for a while?

Bill Dubuque is the winner.

And Robjohn?

Really? What's .blt? And don't say "a sandwich"!

Ыt

@MarkDominus I doubt it ... I defended too many unpopular topics on meta.

Maybe I am interpreting the file incorrectly.

A sandwich.

Bill, you have your thumb on the meta pulse (and not just at MSE) more than anyone.

I had to guess what it meant.

@BillDubuque I know some people who voted for you :)

I put Bill as my first choice.

@MarkDominus What software would you use to open this sandwich file?

@TheChaz: confusing

I used "cat" to look it over, and then perl to get a quick count.

^^ no kidding! I saw that a few minutes ago, then gave up

@MarkDominus So you're serious about the clear #1 choice?

(being Bill)

Hmmm, what election method are we supposed to use here?

It's a text file. Each line seems to have the form "1 X Y Z 0" where X is their first-place vote, Y and Z are second- and third-place votes. X Y and Z are numbers and there is a section at the bottom that maps the numbers to the names.

@zhen: Single transferable vote.

the winners are bill and eric

Then congrats to them!

O ye of little faith!

Wish we could have had three...

me too

@MarkDominus: There are many variants. OpenSTV itself gives a few...

@MarkDominus I just didn't know if you were throwing that out there as wishful thinking or an educated guess!

It was an educated guess based on my offhand guess about the format of the vote total file. Sorry this was unclear.

^

Let's see. Using "Meek STV", Bill is elected in round 1 immediately.

@anon Yes. I just downloaded the data and that is what I see. Is it posted anywhere yet?

@anon Can you upload a screenshot of your software output? (Or @Zhen)

@anon second it

pastebin.com/xRtnG2wq

Thanks, Zhen

@Zhen: thanks

@anon: What does that tabulate?

not sure :<

"approval voting," whatever that is

Approval voting is definitely not the method in use...

I just had it count first-place votes, which was enough to see that Bill was the clear winner and Eric most likely second.

no, that is not approval voting

at least not pure approval voting

Oh, this definitely isn't approval voting. In approval voting, everyone votes for as many candidates as they want, and the candiates with the most votes win.

Amusingly it looks like the first-preference rankings are in order of rep...

Those are what the stats would be in approval voting (though this isn't the case here), I guess.

@anon Is that the total of the first, second, and third votes?

Here, everyone ranks up to three candidates, and the first-choice votes are considered. If there aren't enough winners, the least-favored candidates are eliminated and ballots that voted first-choice for them are converted to voting for their second choices, etc.

@robjohn Looks like it's ~1200 = 3* ~400 (votes)

@TheChaz there were 394 ballots cast.

so that looks about right

(I know!)

Oh right

More precisely, 1116 / 3 = 372, so it would seem not everyone used all three slots.

Tough crowd...

Correct.

38 votes used fewer than 3 slots.

Most of those used only one of the three slots.

So why they don't publish the results?

@BillDubuque I guess it's open season on Bezout jokes :-)

Perhaps several people are tabulating them independently and comparing their tabulations?

Presumably the results have to be approved by people, and then winners officially notified, etc. etc.

@Gigili I put up a tentative post on meta, for those who can't won't see the chat log.

@MarkDominus It's not even really close enough to worry the details. No matter how things are computed, Bill and Eric are the new mods.

So congrats to Bill and Eric!

Indeed. That's why I announced Bill without bothering to even look at the 2nd and 3rd place votes.

About that speech, Bill :D

Yes, congratulations.

We will now establish Number Theory as the official state religion on MSE, as per the overall plan. (cackles)

Bill got 163/394 first-place votes, with 10 candidates; the next best was 74/394 first-place votes. That is a landslide.

throws tomatos

Everyone get your telescopy gloves on!

@ZhenLin Ouch

I mean the number theory!

^^ The comments were split

I'm relieved.

That's a pity that you are not elected, @robjohn.

@MichaelGreinecker Indeed! Congratulations Bill and Eric!

@robjohn Oh you're not our König :-(.

Congratulations Bill and Eric.

My other two choices :-).

Two other people voted exactly the same way I did.

@JonasTeuwen Still the owner of the chat.

@MarkDominus Who was your #2?

@ClarkKent Yeah, right :-p

@ClarkKent there is a mod who owns this room, too.

Though I've never met him.

Why is there such a strong tendency for se.math users to choose abstract avatars?

@robjohn Thanks. It looks like the votes were proprtional to meta-activity, but I can't find the candidates stats page to confirm that. Anyone have a link?

elections.stackexchange.com

@ClarkKent Channeling Dan Quayle (CTRL + F "potato")?

(That will make no sense if you're not from the US... maybe only a little if you are!)

@BillDubuque The two with the highest rep won, it seems.

I like the spelling without <e> better, and my spellchecker doesn't object!

@BillDubuque but my meta activity was so low that I don't think it is proportional

British vs. US English?

@robjohn But that was probably compensated for by your chat rep. Probably some combination of main and meta rep/#answers etc played a large role. I still cannot find the original stats page that SE supplied, which gave different stats.

@robjohn The page I recall had more info from meta included, which is why I thought meta stats may have been influential.

@BillDubuque There is this page.

Well, good luck to all moderators, new, old, fifty-fifty.

I'm off to bed, good night.

I can go back to my mean avatar again :-D

@robjohn: This was your nice avatar?!?

@MichaelGreinecker Indeed! >8(

Eeeek

so are the elections over now?

@DavidWheeler Indeed. Bill and Eric are the new mods.

Eric?

@DavidWheeler Eric Naslund

@robjohn I wish there had been a third spot. I think you would have made an excellent mod (I voted for you)

i don't recognize the name...does he have a different user name?

@DavidWheeler Eric Naslund

I find it a bit strange that a user whose answers/questions/comments I rarely see got elected as a mod.

hmm...i don't recall seeing him when i voted.

@ZhenLin Perhaps he answers questions in topics you don't normally peruse. You probably don't see my answers much, do you?

"Analytic Number Theory and Additive Combinatorics"... so yes.

I see your answers occasionally, but you answer lots of questions!

@ZhenLin Eric has to have answered a lot, too. His rep is higher than mine.

True. shrug

i suppose i should wish Bill congratulations. congratulations. there, my obligatory fawning is done. more will cost you extra.

@ZhenLin Eric has answered 407 Questions, and I have answered 557, so not that great a difference.

I don't like analysis, number theory, or combinatorics... so Eric's interests lie in the intersection of my disinterests!

@ZhenLin those are pretty much my interests, too. Perhaps I pick more lhf, and that is why you see some of mine :-)

I really liked this one

I like all mathematics. I just suck at most of it.

@N3buchadnezzar I commented on that answer. Why are you copying it here?

oh, Jordan is here. no wait, that's Jonas.

I think I need to rethink my exposition. I have somehow managed to talk about the bicategory of spans and the bicategory of profunctors before the bicategory of categories.