The h Bar

Slereah

13:04

you know what else is a sheaf?

QFT.

Or a presheaf, I dunno

What does a sheaf have more than a sheaf

0celouvsky

@Slereah the ability to patch together local data

and the ability to inspect global things by looking locally

what does étalé mean?

Slereah

Do you mean the math thing or the french thing

0celouvsky

in french

Slereah

spread

0celouvsky

a spread space

Slereah

13:07

Are there connections that aren't special case of Ehresmann

0celouvsky

Cartan connections

Slereah

Is it of some use in physics

Or can I ignore it

0celouvsky

ignore

Slereah

DELETED

0celouvsky

it's used for "generalized geometries" in projective spaces and the like

@ACuriousMind To check that something is an abelian group, is it enough to show that it is closed under subtraction?

This guy trying to show that the sections of the etale space of a presheaf of abelian groups is abelian

He shows that it's closed under pointwise subtraction

I guess one can use subtraction to show that $-s$ is also a section

So $t-(-s)=t+s$?

Slereah

13:25

So what is the chat session about today

I hope it's not gonna be that kaon ratio thing

Real snooze fest

Koolman

@Ramanujan For physics you can use physicsgalaxy.com

0celouvsky

sheaves are too hard

Slereah

I mean what were you expecting

doing category theory

Were you expecting bike rides in the park and balloons

0celouvsky

ye

I'm too used to analysis

I guess an isomorphism in an algebraic category is just a bijective homomorphism

It doesn't have to have a homomorphic inverse

Slereah

Learn modal logic instead

0celouvsky

13:29

or maybe that's automatic

who the hell knows

Slereah

Modal logic has like 0 application to math or physics

0celouvsky

@ACuriousMind where are you

Slereah

It's great

I have a whole book on modal logic

I don't think I've ever had to use it for anything

0celouvsky

What is it?

Slereah

It's a model of logic used for a few things

Mostly to describe either certainty or morality

0celouvsky

13:35

such as?

lol

Slereah

For certainty you have the operator $\Box$

A proposition $p$ is necessary if $\Box p$

And you have the operator $\Diamond$ for "possibly"

And the relation $\Diamond p \leftrightarrow \neg \Box\neg p$

If the negation of something isn't necessary, it's possible

The morality semantic is the same idea, except $\Box$ stands for like

Moral obligation

It's basically the least useful field of math I've studied

although the book on it was nice, but more because it showed a lot of methods you can generally use for logic systems

user400188

13:51

the only use I've ever found for modal logic is been able to translate Gödel's ontological argument, which is a neat party trick.

Hmm, actualy; I've wondered for a while now if modal logic could be of any use to the many worlds approch to QM

since we are talking about different worlds and whatnot in it

Slereah

it would not be particularly useful

People already tried to change logic to fit QM better

it's more hassle than it's worth

Secret

14:08

Do we really need to change logic? It is clear that "A and B" does not hold in general in quantum

Slereah

14:39

-7

Q: Does relativity hold in the dark?

I will start with a very often used example to explain the theory of relativity of Einstein, we consider 2 pair mirrors, one will be stationary and the other will be in motion. There will be a light ray in between them. As the mirror moves, the light ray travels more distance from one mirror to t...

Slereah

14:56

Sometimes you find a paper

and you can tell the math wasn't done in Latex

Disgusting

Secret

Joke: I wonder if that will hold in quantum gravity, given how in quantum you don't have the outcomes already determined and must be revealed via measurement

Slereah

15:09

"The tensor bundle $\otimes TM = \bigcup_{x \in M} \bigoplus_{p,q \in \Bbb N} \bigotimes^p_q T_x M$

Whaaat

Sanya

@Slereah you mean like papers from before the time of computers? :D

Slereah

@Sanya no, papers who were probably made with MS Words

paracresol

@JohnR Are Azimuthal Quantum numbers necessarily non-negative integers?

Secret

[My scifi]

I really like to speak in this tone, lol

Please note my current QFT knowledge still sucks thus be aware of nonsensical stuff in that paragraph

Slereah

"In the following, out of comfort, we confine ourselves to real vector bundles (of constant rank)."

Very comfy

Sanya

15:23

@Slereah yuck. My M.Sc. supervisor made me write in word, the equations look horrendous

Bernardo Meurer

@0celouvsky Fantano dropped DAMN review

0celouvsky

15:37

@Slereah what's wrong

@Slereah what are you reading

Slereah

It's quite a series of operators

0celouvsky

@BernardoMeurer ayy

Slereah

Some thing on fiber bundles

0celouvsky

@BernardoMeurer FUCKING SEVEN

Bernardo Meurer

DUDE

WTF

I wan't done yet

you ass

Spoilers

0celouvsky

15:38

sory

Did ACM ever show up?

Jaime Gallego

@Secret Worldbuilding is cool. I used to have a NationStates account and micromanage every nook and cranny of the government.

Slereah

"Here we would like to transfer the second vector “without change” to the fiber of the first. So we need a rule of parallel transport of a vector from one fiber into another. We feel that such a “connection” between fibers should allow to define the covariant derivative of a section s in the direction of a vector field X. "

a """CONNECTION""" you say

very good foreshadowing

Jaime Gallego

@Secret Most of my Adobe skills come from crafting these fictional documents.

user228700

@JohnR: Apparently, I'm receiving a "certificate of merit" from school!

Secret

@JaimeGallego Looks pretty authentic

John Rennie

15:49

@Kaumudi.H Congratulations! What for?

Secret

@JaimeGallego For me, when I do scifi worldbuilding, I often try to keep as much scientific rigor as possible, while not sacrificing those interesting plot elements. The scientific rigor in a sense allow the possibility of most things in my settings to be able to realise when given a chance (e.g. when someone suddenly discover some new physics which is the tiny bit of thing to leap across the gap from imagination to reality)

user228700

@JohnRennie I don't know yet but I suspect it's because I topped in Math in my finals last year.

John Rennie

Cool :-) It took them a while though ...

Secret

In a sense, you may say that I work closely with reality itself on my scifi, and it is one of my consultants

user228700

@JohnRennie :-) They give them out at the Annual Day each year and the results usually come out after it so they hand out these certificates in the succeeding year.

Secret

15:52

This strong dependence on real life is one reason why the story is still unknown for my scifi. In fact, the story is heavily dependent on everyone living on this planet

John Rennie

@Kaumudi.H Do you have to go along and accept your prize in person?

user228700

I'm afraid so :-( I don't feel like going so I hope my dad will be sweet to go and receive it for me.

Secret

My scifi is worldbuilt in a way such that it only take a small nudge to realise most of the things inside. In a sense it is a very ambitious project of blurring reality and fiction to the point that I hope one day even reality itself have trouble telling what is real

user228700

It's on the 21st this year...

Secret

And I should say that, my entire life is dedicated to this goal, for reasons I have yet to figure out

John Rennie

15:54

@Kaumudi.H You're going to send your poor Dad in your place? Gosh, the things we men do for our children :-)

Secret

Most of my passion in physics, unlike chemistry and quantum mechanics, is to obtain the required knowledge to move towards this goal

user228700

:-) I do hope he agrees. I'm practically doomed otherwise.

Secret

And in fact, on can argue why I seemed to know a bit of everything, it is once again geared towards this goal

Bernardo Meurer

@Kaumudi.H I'll go for you

Secret

But perhaps, the interesting question is why did I have such an obssession to blur reality and fiction together so that neither can distinguish from one another

user228700

15:57

@BernardoMeurer Would you really? :-) Man, aren't you somewhere in Brazil? It's quite a way from there to Chennai...

Bernardo Meurer

@Kaumudi.H I live in Portugal now

I will go, not sure when I will arrive though

user228700

Ah, OK. Hmm, the event is on the 21st ._.

0celouvsky

I hope ACM is alive

8

Bernardo Meurer

@Kaumudi.H Get me a plane ticket :P

user228700

@0celouvsky You two are adorable x'D

Jaime Gallego

15:58

@Secret Working toward a goal is an excellent way of learning something.

user228700

@BernardoMeurer :-( I'm totally broke.

Secret

Fooling reality itself is hard, though.

Bernardo Meurer

@Kaumudi.H Build an airplane

Secret

@JaimeGallego Indeed, I recall how back in my grade 10 I learnt about magnetic monopoles simply because I want to include them into my scifi

John Rennie

Haven't we got a chat session now?

Bernardo Meurer

16:01

@JohnRennie No mods, so...

vzn

@JohnRennie yes!

Bernardo Meurer

I DECLARE THE CHAT SESSION ABOUT CARAMEL FUDGE OPEN

John Rennie

@BernardoMeurer Cool, we can talk about anything we like :-)

Bernardo Meurer

Okay people, how do you like your fudge?

user228700

Don't like it.

Bernardo Meurer

16:02

Get out

I'm not getting any award for you

John Rennie

@Kaumudi.H WHAT?!!!!!!

Jaime Gallego

Me neither, but I don't expect an Spanish Inquisition

Bernardo Meurer

@Kaumudi.H Just leave

user228700

:'-(

vzn

lets try to mimic the format. starting with intros. anyone new to the chat room? would you like to introduce yourself?

David Z

16:04

I'm new in that I just came in :-P had a little connection problem

0celouvsky

@Kaumudi.H who?

Bernardo Meurer

@DavidZ How do you like your fudge?

vzn

@DavidZ what a relief, the inmates were running the asylum a few minutes there o_O

David Z

Heh, OK, let's do this for real, 5 minutes delayed.

John Rennie

Actually there is some interesting colloid science involved in making fudge - though I guess that's nearer chemistry than physics.

Bernardo Meurer

16:05

Colloid science is everywhere!

David Z

Belated welcome to everyone to the chat session, etc. etc...

Please keep unrelated discussion until after the scheduled topics

which are, for the moment, our usual: introductions/policy questions/etc, and physics news

If anyone wants to suggest anything else for the agenda, ping me as we go

So as @vzn was saying, anyone new to chat, new to chat sessions, or new to the site?

Jaime Gallego

I am new to chat sessions

user228700

We do have another new-ish person here today/tonight but he hasn't spoken up yet :-) Cough @Para Cough.

David Z

@JaimeGallego hi and welcome, then :-) This is just something we do every couple weeks to get people together in the chat room

paracresol

Hands @Kau a lozenge

David Z

16:08

@paracresol hehe

vzn

@JaimeGallego are you a student? what area?

paracresol

@JohnR Had a look?

51 mins ago, by paracresol

@JohnR Are Azimuthal Quantum numbers necessarily non-negative integers?

Jaime Gallego

@vzn Junior year of Spanish high school, just north of Madrid

John Rennie

@paracresol ... after the chat session is over ...

paracresol

Ah...

tickles @JohnR

So, um... when does the session finish?

David Z

16:10

Yep, for those new, we're a little off our usual procedure today since I came in late. But we have an agenda for these chat sessions which always starts with 5 minutes of introductions (as we've been doing) and 5-10 minutes' discussion of recent physics news, and perhaps other stuff.

0celouvsky

Hello, my name is 0celouvsky

David Z

At the moment let's move on to recent physics news.

Secret

Rubidium spin-orbit coupled bose einstein condenstate with negative effective mass

2

0celouvsky

I am very friendly

paracresol

^ Sure

David Z

16:11

@Secret that one was interesting

Secret

It really sound that dramatic even in the actual journal article itself

vzn

NYC met museum is doing a new math/ physics/ art exhibition

David Z

or, well, it seemed interesting; I didn't get to read the full article

@vzn oh that's cool, do you have a website to link?

vzn

in theory salon, 47 mins ago, by vzn

Where Beauty Meets Math: The Concinnitas Series / met museum

exercise to reader: pick out how many are physics related. did appreciate the P vs NP contribution by Karp myself :)

Slereah

"If the fiber $F$ is contractible, then any fiber bundle $\pi : E \to M$ with fiber $F$ admits global sections."

@0celouvsky can you guess what's written as proof

Sanya

16:14

@Slereah chat session :P

0celouvsky

@Slereah Steenrod 1951

Slereah

@0celouvsky Bingo

"The proofs of these propositions can be found in the classical book by N. Steenrod The topology of fiber bundles, where, in order to decide if a certain bundle admits or not global sections, the obstruction theory is developped."

0celouvsky

@Slereah Eh, you really don't want to know that proof

It has to do with homotopy invariance of pullbacks

Yashas

The message for VLQ flag is "This answer has severe formatting or content problems. This answer is unlikely to be salvageable through editing, and might need to be removed. "

David Z

Well, anyway, we've spent our 10 minutes on physics news

Yashas

16:17

What does content problems mean?

Secret

Electromagnetic duality violated under classical gravitational fields, net polarisation of quantum electromagnetic field is not conserved

David Z

I guess there's not a lot of that this time. So we can go back to open discussion, I suppose.

@Yashas people disagree about that

paracresol

\O/

John Rennie

There was the LHCb presentation this morning ...

Yashas

@DavidZ physics.stackexchange.com/a/327331/60891

wavelength proportional to weight of the light wave

paracresol

16:18

10 hours ago, by GPhys

about 3 hours left until LHCb results presentation: https://indico.cern.ch/event/580620/

Yashas

sounds ridiculous but it was declined

Secret

indico.cern.ch/event/580620

Yashas

" declined - flags should not be used to indicate technical inaccuracies, or an altogether wrong answer "

David Z

I take "content problems" to mean something like "not parseable as English text"

Terry Bollinger

@Secret the abstract for that one reminds me of Dirac's conclusion in his Lectures on QM that curved space is, well, incompatible with quantum mechanics...

paracresol

16:19

Great, so if we're back to open discussion..........@JohnR o/

Yashas

@DavidZ ok that makes sense. ty.

0celouvsky

Slereah

I think I really need to learn what the hell a cohomology is

BAYMAX

any resource guys for SAXS?

0celouvsky

@Slereah

Slereah

16:19

It is proving annoying to not know

Terry Bollinger

@Secret interesting articles you've brought today! Effects that odd likely could have really interesting implications both at theory and someday device levels...

Sanya

@Yashas the problem is that there is a very sloppy slope between "completely bogus" and "not canonical"

David Z

@Yashas sure. Do bear in mind that people differ in their evaluations of flags, but in general, if the only problem with something is that it's wrong (even if it's really wrong) you should go with downvoting it rather than flagging.

Secret

I like odd things, the odder the better

0celouvsky

@Slereah ker/im

Terry Bollinger

16:22

@Secret 'tis the dangling threads that fray most intriguingly, sometimes to the disruption of much.

Sanya

@DavidZ any news on the homework front in the last few months I was away? :D

Secret

But more importantly, understanding why something is odd is more important than recognising it is odd

Terry Bollinger

@Secret Yes!

David Z

@Sanya There was a meta post about it a couple weeks ago or so

vzn

@Secret but not LHV theories! :P

Sanya

16:23

@DavidZ the one by heather?

paracresol

Open question: Are Azimuthal Quantum Numbers necessarily non-negative integers?

David Z

@Sanya yeah, I think so

1

Q: Let's get things rolling again with the homework policy

Okay, so the last time we had a focused discussion of the homework policy was August 2016. Blech. So, let's start thinking about this again. And before you collectively groan, this first post isn't that painful because there's only one thing in here for debate. Let's rename the homework policy....

discussion homework

0celouvsky

which ones are those

Yashas

@paracresol Yes.

0celouvsky

$m$?

or $l$?

Sanya

16:24

@DavidZ yeah, I remember that

0celouvsky

no one actually calls them that

Terry Bollinger

@vzn Local Hidden Variable theory?? Shades of Bell.

vzn

@TerryBollinger right! one of my favorite topics :) ... secret (& many others) has said hes not a fan. :(

Terry Bollinger

@vzn Hmmmmm. Do you accept that experiment forbids true locality -- true hidden variable interpretations -- or nay? I'm very much in the "it not work" category, but I love the overall topic and how Bell approached it. Very methodical, Bell.

As in I mean, pure locality just doesn't seem to match actual experimental results.

I'm not into the homework issue, so I'll mosey along now I guess. I'm having genuine fun writing an intensely computer-perspective long paper. We just don't see the world quite the same way... and at certain levels, that truly starts becoming interesting (or amusing). Hi Emilio! Heading off...

Emilio Pisanty

@Secret aaaaaaand, it seems that one has already made its way to the Wikipedia page for the Alcubierre drive

::facepalm::

or at least it did briefly

Sanya

16:33

@EmilioPisanty well, we could easily spend the next years on a "PSE corrects wiki"-project

Secret

@EmilioPisanty That's poor journalism. Negative effective mass and negative mass are not the same thing

David Z

@Sanya we could actually do some cross-promotion with WikiProject Physics, if people are interested

vzn

@TerryBollinger (sorry something popped up here) have studied this several decades now & think great work both theoretical/ applied/ experimental has been done in the area by very many (incl einstein himself) but think some surprises remain in store. like all the recent work in the area eg "loophole free bell tests"...

John Rennie

Good grief, the prime minister has called a snap election. It would be nice if the government could stop messing around and actually govern.

0celouvsky

What's a snap election

I read that earlier

Also why would you want them to govern

John Rennie

16:39

@0celouvsky maybe it does less harm if they don't :-)

Anonymous

@paracresol Yes, that's by definition. I am curious to know as to why you think it could be negative.

0celouvsky

@JohnRennie that was my point.

paracresol

Um @JohnR quick question?

@blue I don't think that ._.

John Rennie

@paracresol I'm a little distracted ATM so unable to give the Stark effect the concentration it needs ...

Anonymous

@paracresol Then, why did you ask? :P

Secret

16:40

Hydrogen gas generation by hydrothermal activity in enceledus, suggesting microbes can use that as energy source via methanogenesis

paracresol

It's just the "integer" bit that I have an issue with ._.

@JohnRennie Oh no! Drop Stark for now, I pinged you with something else a while ago ;)

0celouvsky

@paracresol what?

paracresol

1 hour ago, by paracresol

@JohnR Are Azimuthal Quantum numbers necessarily non-negative integers?

0celouvsky

You still have not said which ones those are

paracresol

^ Modification: Should they even be integers in the first place?

0celouvsky

16:42

l or m

No one actually calls them that

paracresol

l

John Rennie

@paracresol yes

paracresol

@0celouvsky Really?

Anonymous

@paracresol Wiki Extract: "The azimuthal quantum number arose in the solution of the polar part of the wave equation as shown below."....So definitely it is because the solutions to the equation are whole numbers only. (en.wikipedia.org/wiki/Azimuthal_quantum_number)

0celouvsky

They're nonnegative integers

@paracresol correct

paracresol

16:43

@0celouvsky Wait, so what (else) are they called?

O_o

0celouvsky

The reason is because of the structure of the rotation group

paracresol

O_O

I see...

0celouvsky

You just call them l

paracresol

Lost expression

0celouvsky

Or total angular momentum in the z direction. Something like that

Secret

16:44

Speaking about negative mass (not negative effective mass), I once tried to use this question to show that it is impossible to exist because it will allow perpetual motion

0

Q: Can energy be extracted indefinitely from a mass dipole/mass negative mass pair in perpetual motion?

Some days ago I have read this short piece of article by Hammond which caused me to revisit the theoretical properties of negative mass. It is known that a pair consists of ordinary mass and negative mass of equal magnitude, known as a mass dipole in some sources, can accelerate indefinitely by ...

newtonian-mechanics thermodynamics perpetual-motion

John Rennie

Probably $\ell$ rather than $l$

paracresol

@JohnR what d'ya think about 0celo's proposition there?

John Rennie

@paracresol which one?

paracresol

@JohnRennie "No one really calls it the Azimuthal quantum Number"

ACuriousMind

@0celouvsky I live!

4

0celouvsky

16:45

@ACuriousMind fucking sheaves

John Rennie

@paracresol to be honest atomic structure isn't widely studied once you're past basic QM so we don't refer to it at all :-)

0celouvsky

@paracresol I mean really $\ell$ is just called the "angular momentum"

John Rennie

But azimuthal quantum number is a perfectly good term.

0celouvsky

@JohnRennie Maybe in chemistry

paracresol

Confused

Anonymous

16:47

@paracresol Well, I do call it by that name...coz it is in my syllabus. :P

Anonymous

But $\ell$ is good enough

Balarka Sen

quantum schquantum.

paracresol

@JohnR @0celo You two just slug it out and let me know who wins :3

0celouvsky

It's not called "azimuthal quantum number" in Sakurai

John Rennie

@0celouvsky spectroscopists get excited by these things :-)

0celouvsky

16:47

Hence it's not a real term.

@JohnRennie Except for all the atomic physicists?

paracresol

Look!

I'm changing the topic...

...inconspicuously

ACuriousMind

To weigh in on this highly relevant issue, "azimuthal quantum number" is what you say when you want to sound smart, "angular momentum" is what you say when just talking :P

7

user228700

@para: No need to ping me at The Periodic Table; this chat is quite capable of handling several different conversations at once.

Balarka Sen

capable is the wrong word.

user228700

Forgive me _/\_ What word would you have used, then?

ACuriousMind

16:50

@Kaumudi.H The word is fine, he's just implying this chat isn't very capable ;)

user228700

._. It really is!

paracresol

@Kaumudi.H But we must keep the room alive! Ever since @Jan died, I've been entrusted with that duty!

0celouvsky

A user died?

Btw, I messaged obe and have not heard back.

paracresol

Yeah...pretty much the same way ACM did...

0celouvsky

I do not know what's going on there

paracresol

16:51

52 mins ago, by 0celouvsky

I hope ACM is alive

user228700

@paracresol Eh. I dont' care so much about that. Besides, flirt karna hai, to yahan pe bhi kar sakte ho (I'm sorry that I lapsed into Hindi for a bit; will not happen again...I hope)

paracresol

^ Use your Mother-tongue impostor!

0celouvsky

Ho!

paracresol

(I speaketh not Hindi)

ACuriousMind

I was travelling from visiting my parents over Easter, excuse me I sometimes pretend to have a real life

paracresol

16:52

._.

Balarka Sen

i wish i could speak english

user228700

Hindi is our National language!

0celouvsky

Sakte Ho sounds like an Atlanta skripper

ACuriousMind

@BalarkaSen We all do

paracresol

@Kaumudi.H *Your

Jaime Gallego

16:52

@0celouvsky Shit. I'm getting worried.

user228700

@paracresol You're an Indian -_-

Anonymous

@Kaumudi.H Overexpectations? =P

user228700

@blue Have u been witness to any of our conversations before? I will cite examples if u want but I have a feeling that we should steer away from that :-P

0celouvsky

I'm an Indian

Native Indian

Anonymous

@Kaumudi.H He is a South Polean seal....

Balarka Sen

16:54

you're a Russio-Frenchie

user228700

@0celouvsky Sakte ho = Can do.

paracresol

@JohnR and @0celo, I need to get something straight before I ask you another question... what's the difference (from a physicist's/Mathematician's point of view) between an Operator and a Function?

This post doesn't count:

32

Q: Operator vs function

Could someone please explain the MATHEMATICAL difference between an operator and a function? I am not talking about these in terms of coding but rather the mathematical difference. Is operator also a kind of function? BTW, this is not just a musing and I really need to understand the difference ...

functions terminology operator-theory

Anonymous

@Kaumudi.H Well, I've been around for a couple of months....so yes =D I was just joking :P

ACuriousMind

@0celouvsky Skripper?

Balarka Sen

to put it in simple terms, operator eats functions and spits functions. functions eats numbers and spits numbers

user228700

16:56

@blue Ah, OK :-)

paracresol

@BalarkaSen I really like that :D

ACuriousMind

@BalarkaSen Hmmm? Why would we call linear maps on Hilbert spaces "operators" then?

paracresol

But I need a second opinion...

0celouvsky

An operator takes arguments from a vector space

A function from a set

Secret

If an operator eats functions and spits numbers, it is called a functional

David Z

16:57

@paracresol um, I agree with @BalarkaSen...

for whatever that's worth

ACuriousMind

I don't think there's a definite notion of "operator", some types of functions are simply called operators for historical reasons, I guess

Balarka Sen

@ACuriousMind Well, a vector on a Hilbert space is a linear map, I guess. $w \mapsto \langle v, w\rangle$. But that's a good point.

0celouvsky

I literally just said what it is

No one listens to me

user228700

@0celouvsky :-(

paracresol

@ACuriousMind This one sits well with me :)

BUT

0celouvsky

16:58

Fuck it

And @ACuriousMind ignored all of my pings

user228700

@0celouvsky Aha. Now you know what that feels like!

paracresol

@ACuriousMind Would that apply to the Hamiltonian Operator?

Anonymous

@0celouvsky Most don't understand you...speak simple language like Balarka...hehe =D

0celouvsky

@ACuriousMind oh, but you read that

Smh

ACuriousMind

@0celouvsky I just came in here!

Secret

16:59

n-ary functions (e.g. $f: X_1 \times X_2 \times \cdots \to S $) are the same as multivariable functions?

Balarka Sen

@0celo we put duck tape on our monitors whenever you write a message. but I liked your perspective

2

0celouvsky

@paracresol it's an operator on a Hilbert space

Which is a vector space

Did you not read what I wrote?

paracresol

._.

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