Mathematics - 2017-04-01 (page 3 of 4)

Ted Shifrin

17:00

That makes sense. I did 3 semesters of physics, 1 of biology, some philosophy, but also a whole French major (except for thesis), 5 semesters of German, 2 of Russian, a few English lit classes. I dropped the poly sci and econ classes I started in.

Daminark

Oh right econ's a thing, I might do that, I liked it well enough in high school

Liad

so when did you learned math?

Ted Shifrin

LOL. I took a lot of math.

LeGrandDODOM

Ted is a real humanist

Ted Shifrin

After calculus, I took something like 9 undergrad classes and 6 graduate classes. I might be missing one or two.

That was plenty.

Daminark

17:03

I prob should consider looking at one of the trio of German/French/Spanish

Ted Shifrin

Grad schools are starting to drop the language requirement, Demonark, but I had to demonstrate reading knowledge of 2 of German, French, Russian.

Some schools are allowing programming proficiency now.

Liad

i wish i will learn in the US one day :)

Ted Shifrin

Spanish is useful for the world, Demonark, but not for academic mathematics.

I now wish I were fluent in Spanish.

Liad

@Daminark where do you learn ?

Secret

I still yet to learn python

Balarka Sen

17:04

Spanish literature is awesome cool

Liad

@TedShifrin me too! i want to learn that language

LeGrandDODOM

@Secret ez pz

Ted Shifrin

One of my colleagues and friends before I retired was Israeli, @Liad.

Daminark

I did Spanish, but our class went at a speed that only really gave you vague knowledge of grammatical structures to regurgitate on a test

Secret

@LeGrandDODOM Is it like C?

Daminark

17:05

So really my Spanish is not that good

Liad

@TedShifrin really? from Huji?

Ted Shifrin

si, Demonark :P

Daminark

@Liad I'm in Chicago

LeGrandDODOM

@Secret no, it's completely different. C is much lower-level

Liad

@Secret it is like the opposite of $C $

LeGrandDODOM

17:05

Python is all about getting things done in few lines

Daminark

C traumatized me somewhat, the dang segfaults got on my nerves

Liad

@Secret really fun to learn language

LeGrandDODOM

there are no pointers in python

it's anarchy

Meow Mix

@Secret C is a programming language...

Daminark

Like I'm hesitant now to do a non-functional programming language thanks to C

Meow Mix

17:06

python is a scripting language

LeGrandDODOM

an int is like 1kb

Ted Shifrin

He was on the faculty at Ben Gurion before he came to my university, @Liad.

Hippalectryon

@LeGrandDODOM >import solution; solution()

I love Python though. I've had a horrible experience with Java

Meow Mix

@Hippalectryon But they're totally different.

Liad

@TedShifrin cool. my discrete-math teacher was also from Ben-Gurion , he was a great teacher

Meow Mix

17:07

It's like comparing assembly and Microsoft Excel formula programming

Daminark

Hey @s.harp!

Hippalectryon

Not really, you can do a whole lot of what java can with python @MeowMix

Ted Shifrin

I never have succeeded in programming Excel.

LeGrandDODOM

you know the motto "if java was efficient, it would have been killed by its own garbage collector"

Meow Mix

I can't believe that I can't play my games because of my headphones.

Ted Shifrin

17:09

Zach, you're getting tiresome.

anderstood

@TedShifrin (smoothly merging into the conversation) I recently used javascript to manage google sheets, that's my better than my experience with Excel + VBA

Ted Shifrin

@anderstood: That's cool. I never have been much of a programmer. I came along when programs were still huge stacks of cards (Fortran), and I lost patience. But I have done a reasonable amount of programming in Mathematica (and got reasonably good with TeX/LaTeX).

Daminark

Of the non-math classes you took, which did you like the most @Ted?

LeGrandDODOM

@Ted Fortran is still a thing in 2017 !

Meow Mix

Assembly > *

s.harp

17:11

@Hello @Daminark

Ted Shifrin

I loved literature, particularly French lit courses, Demonark. I also really enjoyed the two physical chemistry courses and freshman physics.

Secret

@LeGrandDODOM It is, very important from molecular calculation scripts to data analysis

anderstood

@TedShifrin I really like Mathematica and use it for most of what I have to do (including parsing webpages ^^). This week-end I'd like to use it to solve the Soma cubes, even though C would be more appropriate...

Secret

My PhD make use of some fotran scripts, which I do nto quite understood

Ted Shifrin

How do you use Mathematica to parse webpages, @anderstood?

s.harp

17:13

@Secret But the only reason it is important is because important codebase uses it. Fortran per se has really no advantage over C

anderstood

@LeGrandDODOM Is Fortran useful when you "know" C / C++?

LeGrandDODOM

From what I heard, it's still used in the US army and banks (old programs that have to be maintained)

Daminark

Nice @Ted

And we are yet again online at the same time @s.harp!

Secret

@s.harp well as far I know, supercomputer structures tend to have fotran scripts somewhere in their folders to organise files and data and schedule jobs, not sure if that is good or bad though.

I found fotran really hard to read because it is just a block of text with // separating sentences

oops sorry

anderstood

@TedShifrin How? Well you can import webpages (MMA might recognize some content and organize it in a pracital way, as lists of string instead of strings), then MMA offers powerful pattern matching possibilities. Nothing you couldn't do with other languages, but I found it more convenient in MMA because of it's high-level features.

Ted Shifrin

17:16

Interesting, @anderstood. Thanks.

Secret

that block of text thing only applies to fotran file outputted by the molecular calculation software gaussian

anderstood

@TedShifrin You can see the example here, to get an idea of what I'm talking about.

Ted Shifrin

Right, I understand. I remember using string syntax in one program long ago.

skull petrol

Are you all set for the final in Miami Prof @TedShifrin?

Ted Shifrin

You know better than that, skull.

skull petrol

17:39

Sorry I've been too busy with the final four happening today :P

nbro

hi guys

question

is it true that whenever we have a problem of the form $Ax = y$, where $A$ is a non-square matrix, then we can never have a unique solution to this problem?

if $A$ is non-square, then we either have more unknowns than equations or viceversa

therefore, if we have more equations, the system is overdetermined

and thus I think we can't have a unique solution

but I'm not sure we can generalize this

there may be exceptions

JeSuis

@TedShifrin D'accord, quand est-ce que cela vous arrange ?

@DanielFischer Hi, say we have two functions $f,g:\Bbb{R}\to \Bbb{R}$ differentiable, and $fg'=0$ does it follow that $fg$ is constant?

SteamyRoot

@nbro Not necessarily.

Consider $$\begin{pmatrix}a_1\\ a_2\end{pmatrix} (x) = \begin{pmatrix}y_1\\y_2\end{pmatrix}$$

which is equivalent to $a_1x = y_1$ and $a_2x = y_2$

Suppose all of $a_1,a_2,y_1,y_2$ are nonzero and $y_1/a_1 = y_2/a_2$

Then there is a unique solution $x = y_1/a_1 = y_2/a_2$

nbro

luckily I had this doubt, then

:D

anderstood

17:56

@nbro It may not be true if the equations are not linearly-independent

Give me a break

18:23

Greetings @Hippalectryon. How are you doing?

Hippalectryon

@Givemeabreak Have you changed usernames ? >.>

Give me a break

@Hippalectryon Yeap, maybe I'll change it soon.

Hippalectryon

:o wait I think I know who you are looking at your MSE profile :D I'm great, what about you ?

Meow Mix

Hi

@Givemeabreak Can you repost the problem with all the zetas?

Give me a break

@Hippalectryon Better times are possible here. In general I'm working on all kind of stuff. Glad to hear you're fine.

@MeowMix Hi. Sure.

Meow Mix

18:27

Sorry :P

Give me a break

$$3\zeta(2)\zeta(5)+\frac{3}{4}\zeta(3)\zeta(4)-6 \zeta(7)>0$$

Hippalectryon

@Givemeabreak How's the book doing ? :D

Give me a break

@MeowMix Did you find a way of proving my inequality?

Meow Mix

maybe I could evaluate each zeta using integrals.

Give me a break

@Hippalectryon I gave up my idea of writing a book.

Hippalectryon

18:29

@Givemeabreak Uh ? How come ?

Give me a break

@Hippalectryon As simply as that.

Hippalectryon

Damn :( I really wanted that book :-)

skull petrol

11

Q: MathJax site going offline

The news that MathJax CDN shutting down on April 30, 2017 was recently brought to my attention. I am testing an updated version of ChatJax which uses the alternate server given in the MathJax post. It seems to work well, but if StackExchange is going to host a local copy to use with the sites t...

Give me a break

@Hippalectryon Maybe you can let me something to contact you one day, when I feel I have something to share with you.

@Hippalectryon ;) no hurry with that, there is time for that

@skullpetrol hey. Curiously I didn't see robjohn around lately

Hippalectryon

He was here mere hours ago

Give me a break

18:39

@MeowMix Let me know if your idea is successful.

@Hippalectryon Perhaps, as I said I come here rarely

Meow Mix

Actually, I could just write out the infinite series

skull petrol

He's busy @Givemeabreak

Who are you?

Aetos

Give me a break

@skullpetrol I do math art

Aetos

someone please, please help me keep my sanity

How does that follow?

Dattier

18:45

$T=5^{5^{5^{...}}}$ a tower with a height of $5^{5^5}$. Find $T\mod 10^5$

skull petrol

The artist?

Give me a break

@skullpetrol Yeap :-)

Back in 10 min.

skull petrol

:D

Meow Mix

@Dattier Let's look at a pattern of $5^x$

Dattier

@MeowMix why not

Meow Mix

18:47

1, 5, 25, 125, 625, 3125, 15625, 78125, 390625, 1953125, 9765625, 48828125, 244140625, 1220703125, 6103515625, 30517578125, 152587890625, 762939453125, 3814697265625, 19073486328125, 95367431640625, 476837158203125, 2384185791015625, 11920928955078125

So no matter what, we know our last digit will be 5.

Correct?

also, the second to last digit must be 2 as well.

Dattier

@MeowMix 1/ok, 2/I don't know, what is you level ?

Meow Mix

what do you mean?

Also, we're just noticing a pattern

Dattier

Licence, maîtrise, college ?

Meow Mix

If you look at all the numbers in those, each has a tens digit of 2.

@Dattier I'm in middle school, but I've studied on my own quite a bit.

That is, each end with "25"

Dattier

it's good. for "25" I will do the calculations

Meow Mix

18:53

@skullpetrol trying to take over

:[

haha

Hi @Ted

@Dattier So the third digit alternates between 1 and 6. do you notice that?

@skullpetrol I was only kidding.

skull petrol

np pal

Ted Shifrin

Rehi Zach

Dattier

@MeowMix : what's the math's tools you know ?

for the integers ?

Ted Shifrin

@Aetos: What part of the scalar curvature question is troubling you? When you wedge with $\omega^{n-1}$, you are going to get only the diagonal terms in Ric, and so, up to constants, we'll get $s\omega^n$. Now the $2/n$ must depend on what the normalization of scalar curvature is.

Dattier

@MeowMix you know the rings ?

Meow Mix

18:59

@Dattier That is beside the point. This problem is nothing more than basic arithmetic.

skull petrol

^

Dattier

@MeowMix : I think knowing how to calculate a rest would not be enough

Meow Mix

Huh? Sorry, I don't understand.

Dattier

I think knowing how to calculate a reminder would not be enough

sorry my english is very bad

Meow Mix

Uhh @Ted can you talk to him in French? I'm not really sure what he means. Sorry to be bothersome :P

@Dattier No, it's not your fault :]

@Dattier You are French, correct?

Dattier

19:02

I hope

Tu es français

Aetos

@TedShifrin Thank you, Ted. I am actually carrying out the computations myself. So, for example, if $\omega=\sqrt{-1}/2\sum_{i=1}^ndz_i\wedge d\bar z_i$ and $\text{Ric}=\sqrt{-1}\sum_{i=1}^nr_{i\bar i}dz_i\wedge d\bar z_i$, then I would like to actually compute $\text{Ric}\wedge\omega^{n-1}$.

Ted Shifrin

You have Ric wrong, @Aetos.

It should be (up to constants) $\sum r_{i\bar j} dz_i\wedge d\bar z_j$.

Zach: I presume he wants to use ring properties of modular arithmetic to prove some rigorous statement by induction.

The point is, @Aetos, that when you wedge with $\omega^{n-1}$, you will pick up only the $dz_i\wedge d\bar z_i$ terms from Ric.

Meow Mix

@Ted oh, like modular exponentiation?

Ted Shifrin

What do you mean by that?

skull petrol

Pardon my interruption @MeowMix

Aetos

19:18

@TedShifrin Could you please elaborate a bit more on why only the $dz_i\wedge d\bar z_i$ terms are picked? I intuitively agree with this statement but I am unable to pinpoint why. For example, up to constants, $\text{Ric}\wedge\omega^{n-1}=(\sum r_{i\bar j}dz_i\wedge d\bar z_j)\wedge(\sum dz_i\wedge d\bar z_i)^{n-1}$.

Ted Shifrin

$n-1$ on the right term

A typical term in $\omega^{n-1}$ has $dz_1\wedge d\bar z_1\wedge ... \wedge dz_n\wedge d\bar z_n$ with precisely one $dz_i\wedge d\bar z_i$ missing.

So you'll pick up exactly that $r_{i\bar i}dz_i\wedge d\bar z_i$ from the Ric term.

Of course you have to keep track of constants.

With all the other terms, you'll have $0$ contribution (either repeated $dz_k$ or repeated $d\bar z_k$).

Best to write out the $n=2$ case first to see it precisely.

I'll be back later ...

Meow Mix

Bye @Ted-o

Aetos

@TedShifrin I will try that. Thank you so much. :)

Sha Vuklia

I have to calculate the eigenvalues and eigenvectors of the following matrix:
$$
A=\begin{pmatrix}
1&1&1&1\\
1&1&1&1\\
1&1&1&1\\
1&1&1&1\\
\end{pmatrix}.
$$
So I want to find $\lambda$ for which $\det(A-\lambda I)=0$. I reduced the problem to:
$$
\begin{vmatrix}
1-\lambda&1&1&1\\
\lambda&-\lambda&0&0\\
\lambda&0&-\lambda&0\\
\lambda&0&0&-\lambda
\end{vmatrix}.
$$
Should I stop here and write out the characteristic polynomial, or is there any other simplification possible? At first I thought it would be alright to start writing out the polynomial from here, but it's getting quite big

well actually

it's doable

I was just lazy

Dattier

@MeowMix : math.stackexchange.com/questions/2213496/…

Semiclassical

19:35

@ShaVuklia From prior experience, the simplest way to do that problem is to write the matrix as the outer product $A=uu^T$ where $u$ is a column vector of 1's.

Sha Vuklia

@Semiclassical i've never thought of it like that. Is there some interesting property of the determinant you can use then?

Semiclassical

There's a useful formula, which I'll look up in a moment.

But the simpler point is that it has a very obvious eigenvector, namely $u$ itself.

Liad

if i have $\int_0^1 dx$ and i use the subtitution $x =sin(t) $ , is it now $\int_0^{\pi/2} cos(t) dt$ ?

Semiclassical

Namely, $Au=uu^T u=(u^T u)u=4u$. So $u$ is the eigenvector corresponding to eigenvalue $4$.

SteamyRoot

Heh

Liad

19:38

im asking about the new boundaries

Meow Mix

How do you do the modular arithmetic triple equal?

Sha Vuklia

ohh, let me think!

Semiclassical

Additionally, any vector $v$ which is orthogonal to $u$ will be an eigenvector as well.

Meow Mix

In LaTeX

SteamyRoot

Also, @Sha: when you said you had reduced the problem to that matrix

Sha Vuklia

19:39

How do you get $uu^Tu=(u^Tu)u$? @Semiclassical

SteamyRoot

you know you can pull factors out of the determinant, right?

Semiclassical

I wondered if that would catch your eye.

The point is really that $(uu^T) u=u(u^T u)$.

(Write out the row/column vectors if you're unsure if this is valid.)

But $u^T u$ is a row vector times a column vector, and therefore is just a scalar.

So we might as well put it in front.

Sha Vuklia

You mean this? @SteamyRoot
$$\begin{vmatrix} 1-\lambda&1&1&1\\ \lambda&-\lambda&0&0\\ \lambda&0&-\lambda&0\\ \lambda&0&0&-\lambda \end{vmatrix}=\lambda^3\begin{vmatrix} 1-\lambda&1&1&1\\ 1&-1&0&0\\ 1&0&-1&0\\ 1&0&0&-1 \end{vmatrix}$$

SteamyRoot

yup

Sha Vuklia

@Semiclassical ah okay! I'm going to write it out for myself!

SteamyRoot

19:42

Now if you just do a few row operations you'll instantly be done

Semiclassical

Anyways, I promised a formula:

Matrix determinant lemma

In mathematics, in particular linear algebra, the matrix determinant lemma computes the determinant of the sum of an invertible matrix A and the dyadic product, u vT, of a column vector u and a row vector vT. == Statement == Suppose A is an invertible square matrix and u, v are column vectors. Then the matrix determinant lemma states that det ( A + u v T ) = ( 1 +...

Sha Vuklia

@SteamyRoot ohhh I see! that is so smart!:) thanks for the hint

Give me a break

@ShaVuklia hi awesome use. How are you doing?

@MeowMix did you get anything with

$$3\zeta(2)\zeta(5)+\frac{3}{4}\zeta(3)\zeta(4)-6 \zeta(7)>0$$ ?

Sha Vuklia

@Semiclassical I see it now! My problem was partially that I use the convention that a vector $v$ is a column vector, so I had everything messed up in my head when I read your formulas:p But thanks! that was nice

Hi @Givemeabreak, how are you?

Semiclassical

Well, that's the same convention I was using.

Give me a break

19:47

@ShaVuklia Just a tiny bit around.

Meow Mix

@Givemeabreak I was busy writing an answer sorry

Sha Vuklia

oh huh that's true. that means that I messed it up twice, so it turned out right:P

sorry it's must be the late hour

Semiclassical

lol

np

Meow Mix

0

A: An infernal tower : $T=5^{5^{5^{...}}}$

Solution using only simple arithmetic and observation Let us look at the digits of powers of $5$, since finding modulo $10^5$ is just finding the last five digits of our tower. First, let's calculate the last digit. Since any power of $5$ has a last digit of $5$, we conclude it must be... well....

Does this look too sloppy?

Semiclassical

So, $u$ is always a right eigenvector of $uu^T$.

Sha Vuklia

19:49

yes, got it!

wait

nm

Semiclassical

What about the other eigenvectors? Well, suppose a column vector $v$ is orthogonal to $u$.

Sha Vuklia

I've never thought or left eigenvectors, but of course that is possible too:P

Semiclassical

Yeah. But worth being precise.

Then $(uu^T)v=u(u^T v)=?$

Sha Vuklia

wait, could you please give me a sec to understand why the other column vector is orthogonal to $u$? I think you wrote that somewhere, so let me reread!

Semiclassical

Well, I'm not saying $v$ 'has to be orthogonal' to $u$. I'm saying: Suppose we find one which happens to be orthgonal to $u$.

Sha Vuklia

19:53

Ahlright

well, then $u(u^Tv)=0$, in other words

our eigenvalue is 0

Semiclassical

Right. So any vector orthogonal to $u$ will also be an eigenvector.

Now, if we were in R^3 then the vectors which are perpendicular to a given vector form a plane.

i.e. a 2D subspace.

Sha Vuklia

yes

Semiclassical

How about in R^4?

Sha Vuklia

it's the same, right?

Semiclassical

No.

Sha Vuklia

19:55

wait

sorry

I misread

wait I know the answer

skull petrol

Slow down and think

Sha Vuklia

it's just a 3D subspace?

Give me a break

@Hippalectryon the process of publishing anything is so slowly sometimes. Waiting for a long period of time to have a kind of special article published. I don't know what is going on with all that delay.

Semiclassical

Right.

So it should be spanned by 3 linearly independent vectors.

Sha Vuklia

because it's the orthogonal complement, and we know it's dimension is 4-1

Semiclassical

19:57

Right.

Sha Vuklia

right, so we know that we have 3 linearly independent vectors for eigenvalue 0

Semiclassical

Right.

Sha Vuklia

and we have one other perpendicular eigenvector $u$

so we've found everything

Semiclassical

yup

Sha Vuklia

niiiiice

!

Semiclassical

19:58

yeeeep

Sha Vuklia

thanks

Give me a break

Let me try a hot chocolate now. Return back in a couple of minutes.

Semiclassical

Another fact to notice, which I think is nice.

Suppose I pick a generic vector $v$ in R^4 (i.e. not in the subspace).

Sha Vuklia

(not) in the $R^3$ subspace you mean?

Semiclassical

right.

Sha Vuklia

19:59

okay

Semiclassical

Then I can decompose it into the two subspaces, i.e. $v=au+bu_{\perp}$ where the second vector is in the orthogonal complement.

Sha Vuklia

yes, I'm with ya

Semiclassical

The action of $uu^T$ on $v$ is then simple: $(uu^T)(au+bu_\perp)=4au$.

So the effect of $uu^T$ is to project $v$ onto the vector $u$ (up to a scaling factor).

So $uu^T$ is a (unnormalized) projection matrix.

Sha Vuklia

ohh right. And if the eigenvalue for $u$ was 1, we'd had the projection matrix on vector $u$

Semiclassical

Right.

In which case the fact that $uu^T$ has the eigenvalues it does is pretty obvious: If your vector is in the subspace generated by $u$, then you get your vector back up to a rescaling.

If it's in the orthogonal complement of $u$, though, it gets annihilated.

Sha Vuklia

20:03

ohhh of course! that's exactly the point of eigenvalues and eigenvectors, isn't it? you can easily see what the matrix (or linear transformation) actually does

Semiclassical

Right.

Sha Vuklia

whoa, this was pretty cool. I've only been doing computations up until now, and I haven't "thought" about the concepts in an exercise. So, many thanks!

Semiclassical

Glad to help.

This is why recognizing the matrix as an outer product is really handy.

Sha Vuklia

haha indeed :P

Semiclassical

It's not always obvious, though.

But it helps when the matrix has some obvious pattern.

Aetos

20:06

@TedShifrin I got it, Ted. Thanks!

Jannik Pitt

I have a quick question: does the complex function z->z^2 preserve circles?

Semiclassical

Circles centered at the origin, yes.

Otherwise, no.

Jannik Pitt

Okay thanks :)

Balarka Sen

20:21

I should probably try to sleep now to reboot the sleep cycle back to normal

whatever normal means

trilolil

Hello everyone!
I am reading this paper about aircraft control systems:http://dspace.ucuenca.edu.ec/bitstream/123456789/21401/1/IEE_17_Romero%20et%20al.pdf
but I am confused about the difference between a transfer and a rotation matrix

on page 3 they show 2 short formulas about those 2 types of matrices

If I understood it correctly

a transfer matrix converts vector from one reference frame to another.

(here velocity vectors).

But doesn't a rotation matrix do exactly the same, i.e. a conversion?

anderstood

21:11

@trilolil Do you know what a rotation matrix is?

trilolil

yes with angles and stuff @anderstood

it contains the angles between two reference systems

it sort of links both reference systems

anderstood

Is T_\Theta a rotation matrix then?

Jannik Pitt

@trilolil It takes in a vector and outputs the same vector rotated by an angle

sashas

math.stackexchange.com/questions/2213643/…\

0

Q: What is wrong with my approach to find an unknown map?

I have a map $f \;A \to B$ and a map $r \;B \to A$ such that $r \circ f = I_{A}$ but $r$ is not inverse of $f$ ie $f \circ r \neq I_{B}$. Now I have to find a map $g$ $C \to A$ such that $f\circ g =h$ where $h$ is a map $C \to B$. So basically I have to find the unknown in the equation $$f \circ...

category-theory

any help please

trilolil

cant a transfer matrix do that @JannikPitt

?

anderstood

21:14

@trilolil Do that what? A rotation matrix has a definition; does T_\Theta satisfy this definition?

trilolil

@anderstood I have read wikipedia, in other words I have read the definition. I came here for clarification not to necessarily to be tested.

Jannik Pitt

@trilolil So what's exactly your question?

@anderstood is just trying to help you

trilolil

@JannikPitt well AFAI have understood and know a rotation matrix can rotate a vector. I also know that a RM can provide some sort of a link between two coordinate systems that are not oriented in the same way (the RM could then provide a transformation from one ref system to another).

On the other side I have understood, from the paper (dspace.ucuenca.edu.ec/bitstream/123456789/21401/1/… paragraph 4 chapter 2.1 ) that a transfer matrix just does a transformation from one reference frame too another. So to me they both seem to do the same. is there a difference?

Meow Mix

21:54

WB @Ted

Ted Shifrin

Re Zach

Meow Mix

Hi @TheGreatDuck

Ted Shifrin

@trilolil: You are right that a rotation matrix is a special sort of transfer matrix (which I assume could be any invertible matrix). Because of the complicated motion of the tradcopter, I infer that linear velocities transform just by the rotation part of the motion, but angular velocities will transform in a more complicated way due to the motion of the moving reference frame.

Still goofing off, Zach?

TheGreatDuck

@MeowMix *high @TedShifrin

Ted Shifrin

hi Duck.

TheGreatDuck

21:58

idk why you'd randomly message me

did you need something?

Ted Shifrin

he's just saying hi ...

TheGreatDuck

@TedShifrin (I wasn't even in the chat when he said hi)

Ted Shifrin

Yeah, we saw your avatar descending into the room.

trilolil

@TedShifrin Thanks!

TheGreatDuck

no seriously. I got a notification from him tagging me which prompted me to come here...

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$Mathematics$ Mathematics