/sci/ - Science & Math » Thread #13387934

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Anonymous Tue 13 Jul 12:34:07 2021 No.13387934 View Reply Original Report

Quoted By: >>13387992 >>13387995 >>13387997 >>13388520 >>13390060 >>13390158 >>13390272 >>13390298 >>13393781 >>13398102 >>13401174 >>13401189

But what IS a vector?

Anonymous

Anonymous Tue 13 Jul 2021 13:00:53 No.13387992 Report

Quoted By: >>13387994 >>13388937 >>13389471 >>13390033 >>13391363

>>13387934
An element of a vector space.

Anonymous

Anonymous Tue 13 Jul 2021 13:02:17 No.13387994 Report

Quoted By: >>13388028 >>13388629 >>13388937 >>13390271

>>13387992
But what IS a vector space?

Anonymous

Anonymous Tue 13 Jul 2021 13:02:49 No.13387995 Report

Quoted By: >>13388937

>>13387934
could be an area

Anonymous

Anonymous Tue 13 Jul 2021 13:03:29 No.13387997 Report

Quoted By: >>13388937

>>13387934
An array of numbers.

Anonymous

Anonymous Tue 13 Jul 2021 13:09:59 No.13388015 Report

Quoted By: >>13388019 >>13389444

(Length, degree_1, degree_2)

Anonymous

Anonymous Tue 13 Jul 2021 13:11:00 No.13388019 Report

Quoted By:

>>13388015
woops, meant angles not degrees.

Anonymous

Anonymous Tue 13 Jul 2021 13:13:48 No.13388028 Report

Quoted By: >>13388496

>>13387994
A space containing vectors

Anonymous

Anonymous Tue 13 Jul 2021 14:51:24 No.13388348 Report

Quoted By:

A spinor with a spin of 1.

Anonymous

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Anonymous Tue 13 Jul 2021 15:18:12 No.13388418 Report

Quoted By:

how do you know it is a vector?

because it transforms like one

Anonymous

Anonymous Tue 13 Jul 2021 15:47:01 No.13388496 Report

Quoted By: >>13388937

>>13388028
A vector space is a space which obeys the vector axioms.

Anonymous

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Anonymous Tue 13 Jul 2021 15:56:40 No.13388520 Report

Quoted By: >>13388545 >>13388550 >>13388937

>>13387934
Here is an intro from my mathematics textbook

Anonymous

Anonymous Tue 13 Jul 2021 16:03:30 No.13388545 Report

Quoted By: >>13388876

>>13388520
That's a terrible introduction

Anonymous

Anonymous Tue 13 Jul 2021 16:06:05 No.13388548 Report

Quoted By:

Vectors are a type of number

Anonymous

Anonymous Tue 13 Jul 2021 16:06:48 No.13388550 Report

Quoted By: >>13388882 >>13388921 >>13388927

>>13388520
>page 675
>JEE
Pooshit garbage

Anonymous

Anonymous Tue 13 Jul 2021 16:18:10 No.13388575 Report

Quoted By: >>13388937

a $\text{GL}(n)$ -equivariant map from the set of frames into $\mathbb{R}^n$

Anonymous

Anonymous Tue 13 Jul 2021 16:31:55 No.13388629 Report

Quoted By:

>>13387994
A module over a field.

Anonymous

Anonymous Tue 13 Jul 2021 17:45:08 No.13388876 Report

Quoted By: >>13388970

>>13388545
Why? Also this textbook is meant for pre college - high school, olympiad students.

Anonymous

Anonymous Tue 13 Jul 2021 17:46:26 No.13388882 Report

Quoted By:

>>13388550
It's a lot better than what passes as a textbook in US

Anonymous

Anonymous Tue 13 Jul 2021 17:59:41 No.13388921 Report

Quoted By:

>>13388550
Also fuck off, I love my textbook.

??? ???? ????????, ??????? ???? ??? ?
??? ??? ?????????????????? ????? ??????? ??????? ?

"Like the crest of the peacock, like the gem on the head of a snake, so is mathematics at the head of all sciences."

Anonymous

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Anonymous Tue 13 Jul 2021 18:02:18 No.13388927 Report

Quoted By: >>13388976 >>13389671

Anonymous

Anonymous Tue 13 Jul 2021 18:04:46 No.13388937 Report

Quoted By: >>13388970 >>13389404 >>13390071

>>13387992
>>13387994
>>13387995
>>13387997
>>13388496
>>13388520
>>13388575
None of you pseuds are being general enough. You assume a vector should start at the origin. A vector is an element of a section of the tangent vector bundle $T \mathbb{R}^n$

Anonymous

Anonymous Tue 13 Jul 2021 18:14:47 No.13388970 Report

Quoted By: >>13389033

>>13388876
>Why?
That's not how a vector is defined in either mathematics or physics, it's just how it's ""defined"" in high school. It also doesn't even try to explain what the difference is between the so-called "physics definition" and "mathematics definition". Dot products and cross products aren't basic operations with vectors, they're additional structures you can define only on certain vector spaces. Overall, it spreads lots of misconceptions.

>>13388937
>complains that others aren't general
>somehow comes up with the least general definition posted in the thread

Anonymous

Anonymous Tue 13 Jul 2021 18:16:40 No.13388976 Report

Quoted By: >>13389039

>>13388927
What country is that in your image?

Anonymous

Anonymous Tue 13 Jul 2021 18:23:25 No.13389000 Report

Quoted By:

It's a set of oriented segments, that have the same magnitude, direction and sense.

Anonymous

Anonymous Tue 13 Jul 2021 18:36:46 No.13389033 Report

Quoted By: >>13389641

>>13388970
What I understood about the physics and mathematical definition is that in physics, they actually define certain quantities as vectors (with direction and magnitude) and scalars (only magnitude), but in mathematics vector is an actual mathematical construct as given, either as directed line segment (geometric) or an ordered pair or triple (algebraic).

Also as I already said this is high school - pre college level textbook

Anonymous

Anonymous Tue 13 Jul 2021 18:38:21 No.13389039 Report

Quoted By: >>13389494

>>13388976
India, that meme depicts an Indian temple and a priest.

That quote I have written is in sanskrit.

Anonymous

Anonymous Tue 13 Jul 2021 20:08:29 No.13389404 Report

Quoted By: >>13389762

>>13388937
>A vector is an element of a section of the tangent vector bundle TRn
a section is not a set of vectors you brainlet retard

Anonymous

Anonymous Tue 13 Jul 2021 20:17:15 No.13389444 Report

Quoted By:

>>13388015
I always forget that $S^1\times S^1=$ a sphere (i know its a torus), thus only needing two angles for a 3d localization

Anonymous

Anonymous Tue 13 Jul 2021 20:23:29 No.13389471 Report

Quoted By: >>13389543

>>13387992
this. where's that "what is flux?" meme when you need it?

Anonymous

Anonymous Tue 13 Jul 2021 20:27:36 No.13389494 Report

Quoted By: >>13389628

>>13389039
Do you speak sanskrit?

Anonymous

Anonymous Tue 13 Jul 2021 20:37:19 No.13389543 Report

Quoted By:

>>13389471
surface integral of a field dotted with the surface normal

Anonymous

Anonymous Tue 13 Jul 2021 20:59:07 No.13389628 Report

Quoted By:

>>13389494
Not in general daily life, but yeah I can recite verses, poems and can speak simple sentences.

Anonymous

Anonymous Tue 13 Jul 2021 21:03:20 No.13389641 Report

Quoted By: >>13389787

>>13389033
Like I said, that's not how they're defined in actual math or physics. I would even say that those definitions are meaningless - why can't scalars have direction? Potential energy can be positive or negative for instance. And "directed line segment" doesn't even make sense for the zero vector so that's not a real definition either.

Anonymous

Anonymous Tue 13 Jul 2021 21:12:02 No.13389671 Report

Quoted By: >>13389811 >>13397967

>>13388927
Indians can't into math. Even Brahmin caste which is supposed to know the basics are completely shit at math.

Anonymous

Anonymous Tue 13 Jul 2021 21:32:29 No.13389762 Report

Quoted By: >>13389973

>>13389404
>a section is not a set of vectors you brainlet retard
A section of a tangent bundle is you double nigger retard

Anonymous

Anonymous Tue 13 Jul 2021 21:38:45 No.13389787 Report

Quoted By: >>13389820

>>13389641
Dude potential energy being negative or positive doesn't have anything to do with direction but difference in magnitude with respect to the chosen reference point.

As for the zero vector, it would be an euclidean point, having zero length and an undefined direction.

Scalars (in physics) can't have direction because that's how they are defined.

Anonymous

Anonymous Tue 13 Jul 2021 21:45:48 No.13389811 Report

Quoted By: >>13397967

>>13389671
> "A later landmark in Indian mathematics was the development of the series expansions for trigonometric functions (sine, cosine, and arc tangent) by mathematicians of the Kerala school in the 15th century CE. Their remarkable work, completed two centuries before the invention of calculus in Europe, provided what is now considered the first example of a power series (apart from geometric series)."

Maybe read history sometimes.
https://en.m.wikipedia.org/wiki/Indian_mathematics

I have nothing but unending respect as far as European mathematicians are considered.

Anonymous

Anonymous Tue 13 Jul 2021 21:49:36 No.13389820 Report

Quoted By: >>13389852

>>13389787
In classical physics, a scalar field is just a real/complex valued function on your space, so it makes sense to speak of its direction at each point (positive/negative).
>undefined direction
So you have to make an exception to the definition particularly for the zero vector then.

Anonymous

Anonymous Tue 13 Jul 2021 22:04:53 No.13389852 Report

Quoted By: >>13389941

>>13389820

I don't see how is it an exception, it's just directed to nowhere.

Imagine two forces cancelling out, we are left with a force with a magnitude zero, that is directed to nowhere.

And this zero vector satisfies all algebraic properties such as the additive property etc.

Anonymous

Anonymous Tue 13 Jul 2021 22:33:21 No.13389941 Report

Quoted By: >>13389977

>>13389852
If the magnitude is 0, you might as well say it's directed left, right, nowhere, everywhere, whatever. Clearly, you'll have problems assigning a direction to the zero vector. Anyway, these definitions might not be totally useless at the high school level despite all their problems but they're certainly not worth considering in any other situation.

Anonymous

Anonymous Tue 13 Jul 2021 22:43:36 No.13389973 Report

Quoted By: >>13392284

>>13389762
I'm not that guy you're replying to but a section is a function not a set right?

Anonymous

Anonymous Tue 13 Jul 2021 22:44:45 No.13389977 Report

Quoted By: >>13390033

>>13389941
Then what according to you would be the perfect definition of a vector?

Anonymous

Anonymous Tue 13 Jul 2021 22:59:13 No.13390033 Report

Quoted By: >>13390040

>>13389977
>>13387992 but with an explanation of what a vector space is. You could probably introduce it in high schools too but in a more informal way. Among the definitions you posted, the one with tuples is slightly better than the others but it's not completely unproblematic either.

Anonymous

Anonymous Tue 13 Jul 2021 23:02:45 No.13390040 Report

Quoted By: >>13390059

>>13390033
But a vector space is any space which obeys the vector axioms - except that informally we only use it for such a space if it contains some vectors. The usual definition is not really constructive.

Anonymous

Anonymous Tue 13 Jul 2021 23:07:55 No.13390059 Report

Quoted By:

>>13390040
Why would a definition have to be constructive? You can construct specific examples of vector spaces anyway.

Anonymous

Anonymous Tue 13 Jul 2021 23:07:58 No.13390060 Report

Quoted By:

>>13387934
We use axioms and derived theorems from those axioms to prove other theorems. You’ve come to the wrong place with your elementary intro to philosophy epistemology. If you can’t accept that we can define further concepts from the axioms, because “muh nihilism” then fuck off to /lit/

Anonymous

Anonymous Tue 13 Jul 2021 23:11:14 No.13390071 Report

Quoted By: >>13390092 >>13390096

>>13388937
A vector has to be within a sub-space. And a sub space has to include the zero vector. You’re talking like you’ve only ever taken physics I. “I drew a line therefore it is a vector” is a F=ma take. We’re doing Ax=b here, pseud.

Anonymous

Anonymous Tue 13 Jul 2021 23:18:50 No.13390092 Report

Quoted By: >>13390102 >>13390151

>>13390071
>is a F=ma take. We’re doing Ax=b here
Not him but wtf does this even mean?

Anonymous

Anonymous Tue 13 Jul 2021 23:19:59 No.13390096 Report

Quoted By: >>13390159

>>13390071
>t. doesn't know differential geometry

Anonymous

Anonymous Tue 13 Jul 2021 23:21:00 No.13390102 Report

Quoted By:

>>13390092
nothing, he's talking nonsense

Anonymous

Anonymous Tue 13 Jul 2021 23:26:24 No.13390115 Report

Quoted By: >>13390146

a line with a point at one extremity, extending by a certain magnitude in a certain direction
a point is a monad given position
a line is breadthless length, or the flux of a point

Anonymous

Anonymous Tue 13 Jul 2021 23:35:53 No.13390146 Report

Quoted By:

>>13390115
>extending
>certain direction

But what if it's the zero vector, Gottfried?

Anonymous

Anonymous Tue 13 Jul 2021 23:39:10 No.13390151 Report

Quoted By:

>>13390092
F=ma is the most basic introduction to physics, and isn’t the entire picture, whereas Ax=b is a fundamental equation in linear algebra, not the watered down garbage they feed the first years in Physics who have no idea what a vector is beyond “a line with direction and magnitude”, which is about as far away from generalized as you can get with a vector other than just referring to it as a list of numbers.

Anonymous

Anonymous Tue 13 Jul 2021 23:42:04 No.13390158 Report

Quoted By:

>>13387934
An element of a vector space

Anonymous

Anonymous Tue 13 Jul 2021 23:42:21 No.13390159 Report

Quoted By: >>13391295

>>13390096
Hell of a take. What part of the literal definition of a vector doesn’t apply to differential geometry? Pxdsa

Anonymous

Anonymous Wed 14 Jul 2021 00:32:06 No.13390271 Report

Quoted By:

>>13387994
1) Closed under addition
2) Closed under scalar multiplcation
3) Includes a additive identity element

Anonymous

Anonymous Wed 14 Jul 2021 00:32:18 No.13390272 Report

Quoted By:

>>13387934
An arrow.

Anonymous

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Anonymous Wed 14 Jul 2021 00:43:04 No.13390298 Report

Quoted By: >>13390447

>>13387934
The enemy of ((((((Gru))))))). And the premises of the movie are shit, nobody becomes a psychopath because mommy is negligent, and pedo jews aren't anti-heroes.

Anonymous

Anonymous Wed 14 Jul 2021 01:44:41 No.13390447 Report

Quoted By: >>13392918

>>13390298
They can play the anti-hero, hero and any other role to manipulate others, but it never results in anything significant and beneficial (except the bare minimum to keep the scam going on), and always has certain obvious limits.

Anonymous

Anonymous Wed 14 Jul 2021 09:14:06 No.13391295 Report

Quoted By:

>>13390159
the person you replied to tried to say that tangent vectors to a Euclidean space based at distinct points are distinguished and need not be based at the origin. the relevance of this (true) statement to the discussion is questionable, but at least it made sense. your comment on that did not.

Anonymous

Anonymous Wed 14 Jul 2021 10:07:48 No.13391363 Report

Quoted By:

>>13387992
few digits

Anonymous

Anonymous Wed 14 Jul 2021 15:32:10 No.13392284 Report

Quoted By:

>>13389973
The result of that function produces a vector field

Anonymous

Anonymous Wed 14 Jul 2021 19:00:28 No.13392918 Report

Quoted By:

>>13390447
They always try to play the role the they believe will be suitable for manipulating others more effectively: fake nice guy, openly evil, fake autist, fake Chad, ...

Anonymous

Anonymous Wed 14 Jul 2021 23:40:56 No.13393781 Report

Quoted By: >>13394177

>>13387934
Hi. CS here. It’s a list of numbers.

Anonymous

Anonymous Wed 14 Jul 2021 23:59:05 No.13393824 Report

Quoted By: >>13395643

Is the "direction" of a vector the same thing as the "order" of a list?

Anonymous

Anonymous Thu 15 Jul 2021 02:08:02 No.13394177 Report

Quoted By:

>>13393781
And a tensor is a list of movie recommendations.

Anonymous

Anonymous Thu 15 Jul 2021 15:05:11 No.13395643 Report

Quoted By: >>13397014

>>13393824
definte order, is this in a mathematical setting?

Anonymous

Anonymous Thu 15 Jul 2021 23:08:17 No.13397014 Report

Quoted By: >>13401130

>>13395643
It would presumably be some type of <, > ordering, but does the specific definition of "order" actually matter in this context? A list with some type of "order" could be said to have a "direction", no? I'm wondering if this idea is analogous to that of a vector

Anonymous

Anonymous Fri 16 Jul 2021 06:27:50 No.13397967 Report

Quoted By:

>>13389671
False and gay.
>>13389811
>I have nothing but unending respect as far as European mathematicians are considered.
Absolutely based and respect-pilled.

Anonymous

Anonymous Fri 16 Jul 2021 07:34:08 No.13398102 Report

Quoted By: >>13401118

>>13387934
vectors gonna vect.

Anonymous

Anonymous Sat 17 Jul 2021 05:13:14 No.13401108 Report

Quoted By:

Before you learn what vector spaces are, think about it as a directed line segment.

Anonymous

Anonymous Sat 17 Jul 2021 05:16:30 No.13401112 Report

Quoted By: >>13401130

Retards, its direction and magnitude. Just as OPs pic guy said in the movie.

Anonymous

Anonymous Sat 17 Jul 2021 05:21:00 No.13401118 Report

Quoted By:

>>13398102
https://en.wikipedia.org/wiki/State_Research_Center_of_Virology_and_Biotechnology_VECTOR#Accidents

Anonymous

Anonymous Sat 17 Jul 2021 05:23:50 No.13401130 Report

Quoted By: >>13401138

>>13401112
Hi, this guy here >>13397014
Can you define "direction"? That was my initial question in this thread. What the fuck is direction?

Anonymous

Anonymous Sat 17 Jul 2021 05:28:14 No.13401138 Report

Quoted By: >>13401149

>>13401130
Not him but a direction is a point on the unit sphere.

Anonymous

Anonymous Sat 17 Jul 2021 05:33:15 No.13401149 Report

Quoted By: >>13401156

>>13401138
Good answer, but that implies you already established some kind of axis/coordinate system. If I give you just a sphere with a dot on it, what can you tell me about the position of the dot?

Anonymous

Anonymous Sat 17 Jul 2021 05:39:06 No.13401156 Report

Quoted By:

>>13401149
>but that implies you already established some kind of axis/coordinate system
Not really. Given a vector space with the notion of a norm, for each non-zero vector v you can form the unit vector v / || v|| which is a point/vector on the unit sphere corresponding to v. Any non-zero vector can be uniquely specified by mentioning its "direction" (corresponding point on the unit sphere) and length. This obviously doesn't apply to vector spaces without a specified norm.
>If I give you just a sphere with a dot on it, what can you tell me about the position of the dot?
I don't understand this question. What kind of information are you expecting about the position of the dot?

Anonymous

Anonymous Sat 17 Jul 2021 05:53:40 No.13401174 Report

Quoted By:

>>13387934
A poor mans quaternion.

Anonymous

Anonymous Sat 17 Jul 2021 06:01:05 No.13401189 Report

Quoted By:

>>13387934
> when the thread gets filled with trash who loves drama and hates behaving properly

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