/sci/ - Science & Math » Thread #13278557

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Anonymous Mon 14 Jun 22:42:37 2021 No.13278557 View Reply Original Report

Quoted By: >>13278561 >>13278565 >>13278640 >>13278647 >>13278651 >>13278740 >>13278746 >>13278852 >>13279347 >>13279371 >>13279378 >>13279382 >>13280264 >>13280326 >>13280339 >>13280387 >>13280999 >>13281148 >>13281563

What is tensor?

Anonymous

Anonymous Mon 14 Jun 2021 22:44:06 No.13278560 Report

Quoted By: >>13278581

A matrix. Everyone below me is a tranny.

Anonymous

Anonymous Mon 14 Jun 2021 22:44:10 No.13278561 Report

Quoted By:

>>13278557
Math

Anonymous

Anonymous Mon 14 Jun 2021 22:45:30 No.13278565 Report

Quoted By:

>>13278557
bondburger is better

Anonymous

Anonymous Mon 14 Jun 2021 22:54:18 No.13278581 Report

Quoted By: >>13278853

>>13278560
Why don't they just call it a matrix then?

Anonymous

Anonymous Mon 14 Jun 2021 23:06:24 No.13278611 Report

Quoted By: >>13278626

It is actually just a name used for anything that behaves like how a tensor is
supposed to behave.

Anonymous

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Anonymous Mon 14 Jun 2021 23:12:03 No.13278626 Report

Quoted By:

>>13278611
>What is tensor?
>It is actually just a name used for anything that behaves like how a tensor is supposed to behave.

Anonymous

Anonymous Mon 14 Jun 2021 23:17:13 No.13278640 Report

Quoted By:

>>13278557
An element of a tensor space.
A tensor space formed $V\otimes W$ from two vector spaces injects into the plain product of those vector spaces $V\times W$ .
And, unlike the pairs $(v, w)\in V\times W$ in the plain product, the tensor space has the property that its elements $v \otimes w \in V\otimes W$ fulfill the linearity [/math]c·v \otimes w = v \otimes c·w[/math]. There's more technicalities but thats how you can tell things apart.
The transformation business is enforced once you do geometry.

Anonymous

Anonymous Mon 14 Jun 2021 23:20:02 No.13278647 Report

Quoted By: >>13278724 >>13279785

>>13278557
An element of a tensor space.

A tensor space $V\otimes W$ formed from two vector spaces can be thought of as a quotient (i.e. is smaller than) the plain product of those vector spaces, $V\times W$ .
And, unlike the pairs $(v, w)\ \in \ V\times W$ in the plain product, the tensor space has the property that its elements $v \otimes w\ \in\ V \otimes W$ fulfill the linearity $c·v \otimes w = v \otimes c·w$ .

Anonymous

Anonymous Mon 14 Jun 2021 23:20:52 No.13278651 Report

Quoted By:

>>13278557
A vector but arranged in a certain way.

Anonymous

Anonymous Mon 14 Jun 2021 23:52:07 No.13278724 Report

Quoted By: >>13279310

>>13278647
This is not true. The dimension of the tensor product is the product of the dimensions, while the dimension of the cross product is the sum of the dimensions, so the cross product can't be a quotient of the tensor product

Anonymous

Anonymous Tue 15 Jun 2021 00:01:12 No.13278740 Report

Quoted By: >>13278931

>>13278557
last night i frog breaded your sister?

Anonymous

Anonymous Tue 15 Jun 2021 00:04:21 No.13278746 Report

Quoted By:

>>13278557
I Pepe sliced your sister?

Anonymous

Anonymous Tue 15 Jun 2021 00:50:00 No.13278852 Report

Quoted By:

>>13278557
Nth dimensional array with computation rules between each other.

Like you multiply matrix so there are rules.

However, I really don't know how to properly multiply or convolve 3D structure, because printer attitude seems bullish.

Or I know and I don't know whwat's proper.

I refuse to generate own 3D data, just to convolve it...

I know a tech, how to recognize objects even in 4D tensors, when there's like tissue density or other medicinal approach by learning machine, but I really don't know how to do that with machine learning.

It's different. You know that.

Otherwise, it's cube of vectors, probably in sane space.

Anonymous

Anonymous Tue 15 Jun 2021 00:51:03 No.13278853 Report

Quoted By:

>>13278581
Nightmares.

Anonymous

Anonymous Tue 15 Jun 2021 01:17:18 No.13278931 Report

Quoted By: >>13281241

>>13278740
I think it's pepe bread
like bred with your peepee

Anonymous

Anonymous Tue 15 Jun 2021 03:15:43 No.13279310 Report

Quoted By: >>13279372

>>13278724
You've got what they said backwards

Anonymous

Anonymous Tue 15 Jun 2021 03:18:02 No.13279324 Report

Quoted By:

I nazi loafed your sister?

Anonymous

Anonymous Tue 15 Jun 2021 03:25:22 No.13279347 Report

Quoted By:

>>13278557
I bred your sister (like a retard)?

Anonymous

Anonymous Tue 15 Jun 2021 03:33:28 No.13279371 Report

Quoted By:

>>13278557
Last night I sliced your sister.

Anonymous

Anonymous Tue 15 Jun 2021 03:33:32 No.13279372 Report

Quoted By:

>>13279310
I typed what I meant to say backwards. The cross product is not a quotient of the tensor product

Anonymous

Anonymous Tue 15 Jun 2021 03:35:03 No.13279378 Report

Quoted By:

>>13278557
Last night I
>sniff bread slice
your sister?

Anonymous

Anonymous Tue 15 Jun 2021 03:35:39 No.13279382 Report

Quoted By:

>>13278557
Unironically an array of numbers. Let $V \cong \mathbb{R}^d$ . Suppose I pick an arbitrary collection of $d^{r+s}$ real numbers, $r, s \in \mathbb{N}$ , and denote them by $T_{j_1 \cdots j_s}^{i_1 \cdots i_r} \in \mathbb{R}$ . Each index ranges in $[d] \equiv \{1, \ldots, d\}$ and corresponds to an arbitrary ordering of this collection.
Then I can always find some orthonormal basis $\{e_j \mid j \in [d]\} \subset V$ , with its canonical dual basis $\{f^i \mid i \in [d]\} \subset V^*$ satisfying $f^i(e_j) = \delta^i_j$ , such that there exists a multilinear map $F : (V^*)^r \times V^s \to \mathbb{R}$ satisfying $F(f^{i_1}, \ldots, f^{i_r}, e_{j_1}, \ldots, e_{j_s}) = T_{j_1 \cdots j_s}^{i_1 \cdots i_r}$ for all of the $d^{r+s}$ chosen real numbers. $F$ is the definition of an $(r, s)$ tensor, while $T$ is an $(r+s)$ -dimensional array of numbers. Hence $F$ can be represented by $T$ .

Anonymous

Anonymous Tue 15 Jun 2021 06:54:25 No.13279785 Report

Quoted By: >>13279792

>>13278647
Is this a joke?

Anonymous

Anonymous Tue 15 Jun 2021 07:00:33 No.13279792 Report

Quoted By:

>>13279785
What are you talking about? It's basically correct if you replace "quotient of V x W" by "quotient of the free vector space generated by V x W"

Anonymous

Anonymous Tue 15 Jun 2021 10:43:23 No.13280264 Report

Quoted By:

>>13278557
A multilinear map from a vector space and it's dualspace to the scalar field /thread.

Anonymous

Anonymous Tue 15 Jun 2021 11:23:40 No.13280326 Report

Quoted By:

>>13278557
an object that shares properties independently of chosen coordinate system

Anonymous

Anonymous Tue 15 Jun 2021 11:30:32 No.13280339 Report

Quoted By:

>>13278557
Last night I green yeasted your sister.

Anonymous

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Anonymous Tue 15 Jun 2021 12:13:41 No.13280387 Report

Quoted By:

>>13278557
https://www.youtube.com/watch?v=aibZkcOsmcE

Anonymous

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Anonymous Tue 15 Jun 2021 16:02:22 No.13280999 Report

Quoted By:

>>13278557
"Last night I pepe bread your sister"? What does it even mean?

Anonymous

Anonymous Tue 15 Jun 2021 16:54:17 No.13281148 Report

Quoted By:

>>13278557
n dimensional matrix

Anonymous

Anonymous Tue 15 Jun 2021 17:30:12 No.13281241 Report

Quoted By:

>>13278931
that's not pepe
so many newfags

Anonymous

Anonymous Tue 15 Jun 2021 18:47:15 No.13281423 Report

Quoted By:

how are there 3 "what is tensor" shitposts up at a time?
is this sneedposting on /sci/?

Anonymous

Anonymous Tue 15 Jun 2021 19:15:50 No.13281524 Report

Quoted By:

Mathfags like to feel pseudointellectually smug over definitions of tensors but yeah it's just something like a matrix.

Anonymous

Anonymous Tue 15 Jun 2021 19:29:02 No.13281563 Report

Quoted By:

>>13278557
idk
t. biology phd student

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