/sci/ - Science & Math » Thread #14230954

25KiB, 800x800, 800px-Complex_number_illustration.svg.png

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Anonymous Tue 15 Feb 05:49:24 2022 No.14230954 View Reply Original Report

Quoted By: >>14231006 >>14231275 >>14231700 >>14233443 >>14233514 >>14233910

Is this a vector?

Anonymous

Anonymous Tue 15 Feb 2022 05:52:00 No.14230956 Report

Quoted By: >>14231044 >>14231055 >>14231505 >>14231649 >>14233487

>PNG
I don't think so.

Anonymous

Anonymous Tue 15 Feb 2022 06:13:38 No.14231006 Report

Quoted By: >>14233602

>>14230954
yes

Anonymous

Anonymous Tue 15 Feb 2022 06:38:44 No.14231044 Report

Quoted By:

>>14230956
stfu nerd

Anonymous

Anonymous Tue 15 Feb 2022 06:44:31 No.14231055 Report

Quoted By:

>>14230956
Kek.

Anonymous

Anonymous Tue 15 Feb 2022 08:54:52 No.14231274 Report

Quoted By: >>14231540 >>14233610 >>14237104

its a matrix
$\begin{pmatrix}<br /> a & -b \\<br /> b & a <br /> <br />\end{pmatrix}$

Anonymous

Anonymous Tue 15 Feb 2022 08:55:57 No.14231275 Report

Quoted By: >>14231283 >>14231284 >>14231488 >>14234729

>>14230954
Yes. Everything in math is a vecor.

Anonymous

Anonymous Tue 15 Feb 2022 09:00:12 No.14231283 Report

Quoted By:

its 2 by2 real matrix that behaves like 2-vector that behaves like single number.
>>14231275
list of numbers

Anonymous

Anonymous Tue 15 Feb 2022 09:00:26 No.14231284 Report

Quoted By: >>14231318 >>14231552 >>14231916

>>14231275
0 isn't

Anonymous

Anonymous Tue 15 Feb 2022 09:25:29 No.14231318 Report

Quoted By:

>>14231284
it's an element of a vector space

Anonymous

Anonymous Tue 15 Feb 2022 11:46:49 No.14231488 Report

Quoted By: >>14231517

>>14231275
>never studied manifolds.
Ngmi

Anonymous

Anonymous Tue 15 Feb 2022 12:01:09 No.14231505 Report

Quoted By:

>>14230956
fpbp

Anonymous

Anonymous Tue 15 Feb 2022 12:12:14 No.14231517 Report

Quoted By: >>14233407

>>14231488
Give me a definition of a vector and an example of an object related to manifolds which doesn't satisfy this definition.

Anonymous

Anonymous Tue 15 Feb 2022 12:37:39 No.14231540 Report

Quoted By:

>>14231274
Only correct answer

Anonymous

Anonymous Tue 15 Feb 2022 12:45:15 No.14231552 Report

Quoted By:

>>14231284
>He hasn't heard of zero vectors
ngmi

Anonymous

Anonymous Tue 15 Feb 2022 13:03:08 No.14231572 Report

Quoted By:

No: it is a poorly drawn diagram seemingly intended to explain the real and imaginary values of a complex number.

Anonymous

Anonymous Tue 15 Feb 2022 14:11:06 No.14231649 Report

Quoted By:

>>14230956
OP btfo

Anonymous

Anonymous Tue 15 Feb 2022 14:22:05 No.14231670 Report

Quoted By:

It's the sum of a scalar and a bivector.

Anonymous

Anonymous Tue 15 Feb 2022 14:37:02 No.14231700 Report

Quoted By:

>>14230954
No, it's a plane.

Anonymous

Anonymous Tue 15 Feb 2022 16:00:00 No.14231916 Report

Quoted By:

>>14231284
>what are 0 vectors

Anonymous

Anonymous Wed 16 Feb 2022 00:04:08 No.14233407 Report

Quoted By: >>14233633

>>14231517
Make a manifold itself into a vector.

Anonymous

Anonymous Wed 16 Feb 2022 00:17:18 No.14233443 Report

Quoted By:

>>14230954
it is if you put it in a vector space

Anonymous

Anonymous Wed 16 Feb 2022 00:30:13 No.14233487 Report

Quoted By:

>>14230956
i lost

Anonymous

Anonymous Wed 16 Feb 2022 00:39:03 No.14233514 Report

Quoted By:

>>14230954
Read the definition of vector space.
A the complex field is also a vector space.

Anonymous

Anonymous Wed 16 Feb 2022 01:10:33 No.14233602 Report

Quoted By:

>>14231006

Anonymous

Anonymous Wed 16 Feb 2022 01:12:12 No.14233610 Report

Quoted By: >>14234629 >>14234899

>>14231274
matrices are vectors

Anonymous

Anonymous Wed 16 Feb 2022 01:19:25 No.14233633 Report

Quoted By:

>>14233407
element of the free vector space generated by any set containing the manifold

Anonymous

Anonymous Wed 16 Feb 2022 02:56:00 No.14233910 Report

Quoted By: >>14233967

>>14230954
fascinating. a zero hypotenuse.
all major mathematics advance has been made by expanding the number system.
i'm a brainlet. grow up and deliver you self important geeks. find an expansion to the number system. natural (counting), rational, irrational, the reals (Dedekind Cuts), imaginary/complex.
What axioms are next? Fuck your axiom of choice. your chatting w a brainlet who is deeply and sincerely interested. Trolls begone.

Anonymous

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Anonymous Wed 16 Feb 2022 03:32:54 No.14233967 Report

Quoted By: >>14233977 >>14234240 >>14236943

>>14233910
>What axioms are next?
For your zero hypotenuse triangle, you'd need to reconcile with the fact that there's division by zero. Sine of alpha is $\frac{1}{0}$ and sine of beta is $\frac{i}{0}$ . And then you'd need to figure out what kind of an angle produces this result. And also commutativity and associativity must be abandoned for some trigonometric identities to work with this new division by zero.

maybe start by solving that

Anonymous

Anonymous Wed 16 Feb 2022 03:37:42 No.14233977 Report

Quoted By: >>14235027 >>14235040

>>14233967
These triangles are used all the time in geometry over finite fields. There are nontrivial spheres of radius 0.

Anonymous

Anonymous Wed 16 Feb 2022 05:38:01 No.14234240 Report

Quoted By:

>>14233967
Just develop some axioms that don't have a problem with any of that

Lol your biggest problem is you're using math that someone else made for something else. Of course it doesn't work.

Anonymous

Anonymous Wed 16 Feb 2022 09:59:06 No.14234629 Report

Quoted By: >>14234631

>>14233610
cats are dogs

Anonymous

Anonymous Wed 16 Feb 2022 10:02:25 No.14234631 Report

Quoted By: >>14234646

>>14234629
Name one matrix which isn't a vector

Anonymous

Anonymous Wed 16 Feb 2022 10:14:35 No.14234646 Report

Quoted By: >>14234688

>>14234631
now you claim
"vector of row vectors"
or
"array of vectors"

im not stupid

Anonymous

Anonymous Wed 16 Feb 2022 10:42:42 No.14234688 Report

Quoted By: >>14234753

>>14234646
so you can't and your analogy was stupid. good.

Anonymous

Anonymous Wed 16 Feb 2022 11:07:33 No.14234729 Report

Quoted By: >>14234735

>>14231275
Is an element of a module over a non commutative ring also a vector?

Anonymous

Anonymous Wed 16 Feb 2022 11:13:32 No.14234735 Report

Quoted By: >>14234754

>>14234729
Yes

Anonymous

Anonymous Wed 16 Feb 2022 11:29:03 No.14234753 Report

Quoted By: >>14234754

>>14234688
usually we think vectors are
$\mathbb{R}^{n\times 1}$
and
matrices are
$\mathbb{R}^{m\times n}$
where m and n both can be one or more.
so, if we take
$A \in \mathbb{R}^{2\times 2}$
this shouldn't be considered a vector, but in neo soj math you can do anything so here we are, cats are dogs.

Anonymous

Anonymous Wed 16 Feb 2022 11:30:48 No.14234754 Report

Quoted By: >>14234757 >>14234801

>>14234735
Make it into one
>>14234753
Holy mother of brainlets.

Anonymous

Anonymous Wed 16 Feb 2022 11:34:33 No.14234757 Report

Quoted By:

>>14234754
holy mother of neo soj math

Anonymous

Anonymous Wed 16 Feb 2022 12:08:45 No.14234801 Report

Quoted By: >>14234900 >>14234931

>>14234754
>Make it into one
It's an element of a vector space, isn't it?

Anonymous

Anonymous Wed 16 Feb 2022 12:51:19 No.14234899 Report

Quoted By:

>>14233610
Not the kind of vectors OP is referring to.

Anonymous

Anonymous Wed 16 Feb 2022 12:52:09 No.14234900 Report

Quoted By: >>14234972

>>14234801
A module isn't a vector space

Anonymous

Anonymous Wed 16 Feb 2022 13:04:07 No.14234931 Report

Quoted By: >>14235274

>>14234801
Any set can be an element of a vector space.

Anonymous

Anonymous Wed 16 Feb 2022 13:35:33 No.14234972 Report

Quoted By:

>>14234900
Its elements are still members of a vector space

Anonymous

Anonymous Wed 16 Feb 2022 14:13:38 No.14235027 Report

Quoted By: >>14235040

>>14233977
Am I alone here among the bots? Am I a bot? Every time that stupid picture of the triangle with hypotenuse 0 is posted I point out that actual mathematicians use this, but I am always ignored completely.

Anonymous

Anonymous Wed 16 Feb 2022 14:21:44 No.14235040 Report

Quoted By:

>>14233977
>>14235027
just cause it has an arbitrary function doesnt mean that a shape with a length of zero is still a meme

Anonymous

Anonymous Wed 16 Feb 2022 15:55:49 No.14235274 Report

Quoted By: >>14235490

>>14234931
lmao what? youre just typing random words at this point

Anonymous

Anonymous Wed 16 Feb 2022 17:00:02 No.14235490 Report

Quoted By:

>>14235274
Lmao are you retarded? Give one example of a set which isn't an element of a vector space.

Anonymous

Anonymous Wed 16 Feb 2022 23:42:52 No.14236943 Report

Quoted By:

>>14233967
that pic... like anons have said, complex math is analogous to a vector space. the hypotenuse is root 2 just interpret the imaginary unit as a second real number line.

Anonymous

Anonymous Thu 17 Feb 2022 00:33:43 No.14237104 Report

Quoted By:

>>14231274
Actually, it's a tensor
$a e_1 \otimes e_1 - b e_1 \otimes e_2 + b e_2 \otimes e_1 + a e_2 \otimes e_2$

Anonymous

Anonymous Thu 17 Feb 2022 02:35:04 No.14237452 Report

Quoted By: >>14239087

it's literally just a vector, by definition. this thread is retarded

Anonymous

Anonymous Thu 17 Feb 2022 15:48:50 No.14239087 Report

Quoted By:

>>14237452
How do you divide by vector?

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