/sci/ - Science & Math » Thread #12780550

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Linear Algebro Wed 03 Mar 14:41:13 2021 No.12780550 View Reply Original Report

Quoted By: >>12780652 >>12780657 >>12781773 >>12784074 >>12785747 >>12793769 >>12793784

mfw The set of all Linear Maps from V to W is a vector space.

Linear Algebro

Linear Algebro Wed 03 Mar 2021 15:05:42 No.12780652 Report

Quoted By: >>12781344 >>12783708

>>12780550
So I guess L(V,W) is a vector space over itself no? I wonder what L(V,W)^2 represents, I guess that's just the set of all functions from {1,2} to L(V,W) which is sorta useless I assume idk I'm super excited to learn more about this stuff.

Anonymous

Anonymous Wed 03 Mar 2021 15:07:51 No.12780657 Report

Quoted By: >>12780664

>>12780550

Neat, isn't it?

Enjoy learning this stuff anon :D

Linear Algebro

Linear Algebro Wed 03 Mar 2021 15:09:44 No.12780664 Report

Quoted By:

>>12780657
I know right, I just peaked ahead in my LA textbook and this tiny tidbit has seriously brightened my day and I gotta spread the love somehow

Anonymous

Anonymous Wed 03 Mar 2021 17:20:48 No.12781344 Report

Quoted By: >>12785982 >>12786312 >>12793764

>>12780652
>So I guess L(V,W) is a vector space over itself no?
no. how could it be a vector space over something which is not a field?

Anonymous

Anonymous Wed 03 Mar 2021 18:19:11 No.12781773 Report

Quoted By:

>>12780550
Literally everything is a vector space/module

Anonymous

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Anonymous Wed 03 Mar 2021 21:40:01 No.12783554 Report

Quoted By: >>12783683 >>12783730 >>12793938

>tfw you take a matrix vector space function and throw billions of random garbage data points in there
>it can suddenly understand language and develops math skills
wtf brehs

Linear Algebro

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Linear Algebro Wed 03 Mar 2021 22:04:47 No.12783683 Report

Quoted By: >>12783730

>>12783554
Excuse me?

Anonymous

Anonymous Wed 03 Mar 2021 22:09:26 No.12783708 Report

Quoted By:

>>12780652
You are never going to make it

Anonymous

Anonymous Wed 03 Mar 2021 22:12:43 No.12783730 Report

Quoted By: >>12783905 >>12783991 >>12784061 >>12784203 >>12785755

>>12783554
>>12783683
It's just a very large set of matrices with hundreds or thousands of free parameters to optimize. It doesn't understand language.

Anonymous

Anonymous Wed 03 Mar 2021 22:40:17 No.12783905 Report

Quoted By:

>>12783730
Not yet anon, not yet.

Anonymous

Anonymous Wed 03 Mar 2021 22:51:08 No.12783991 Report

Quoted By:

>>12783730
This is why they don't build software to monitor their baby AI. Nobody will invest when they find it is only shit in those diapers.

Anonymous

Anonymous Wed 03 Mar 2021 22:56:51 No.12784061 Report

Quoted By:

>>12783730
how do you know what it does and doesn't understand? How is it any different from your own brain?

Anonymous

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Anonymous Wed 03 Mar 2021 22:58:19 No.12784074 Report

Quoted By: >>12784235 >>12786069

>>12780550
mfw no canonical isomorphism between $V$ and $V^*$

Anonymous

Anonymous Wed 03 Mar 2021 23:10:46 No.12784203 Report

Quoted By:

>>12783730
I think "understand" is a loaded word, but how do you explain language models being able to do basic arithmetic outside of its learning table or converting text into simple code? There's seemingly some kind of emergent phenomenon I wouldn't personally expect from something that just tries to predict the next word in a sequence.

Anonymous

Anonymous Wed 03 Mar 2021 23:12:51 No.12784235 Report

Quoted By: >>12788228

>>12784074
Theres not even a noncanonical isomorphism between V and V star. The spaces are completely different.

Anonymous

Anonymous Thu 04 Mar 2021 01:37:58 No.12785747 Report

Quoted By:

>>12780550
0_o

Anonymous

Anonymous Thu 04 Mar 2021 01:39:58 No.12785755 Report

Quoted By: >>12795530

>>12783730
^ nobody tell him how his brain roughly works

Anonymous

Anonymous Thu 04 Mar 2021 02:32:50 No.12785982 Report

Quoted By:

>>12781344
my penis is a isomorphism from my fupa to your mom's mouth

Anonymous

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Anonymous Thu 04 Mar 2021 03:02:51 No.12786069 Report

Quoted By: >>12792544

>>12784074
>mfw V is an inner product space and there is a non-degenerate bilinear map VxV-> F.

Linear Algebro

Linear Algebro Thu 04 Mar 2021 04:11:27 No.12786312 Report

Quoted By: >>12786490 >>12786711 >>12788223 >>12793790

>>12781344
What? How is L(V,W) not a field?
there's a notion of addition and multiplication of its elements
multiplication distributes over addition
there are inverses and identities

Anonymous

Anonymous Thu 04 Mar 2021 05:06:26 No.12786490 Report

Quoted By: >>12786498

>>12786312
there's no multiplication

Linear Algebro

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Linear Algebro Thu 04 Mar 2021 05:08:55 No.12786498 Report

Quoted By: >>12786506

>>12786490

Anonymous

Anonymous Thu 04 Mar 2021 05:10:53 No.12786506 Report

Quoted By: >>12786998 >>12788173

>>12786498
Not a multiplication on L(V,W)

Anonymous

Anonymous Thu 04 Mar 2021 06:32:12 No.12786711 Report

Quoted By: >>12786731

>>12786312
>How is L(V,W) not a field?
Hint: think

Anonymous

Anonymous Thu 04 Mar 2021 06:41:37 No.12786731 Report

Quoted By:

>>12786711
dubs of truth

Anonymous

Anonymous Thu 04 Mar 2021 08:21:36 No.12786998 Report

Quoted By: >>12787202

>>12786506
shut up brainlet

Anonymous

Anonymous Thu 04 Mar 2021 09:16:27 No.12787202 Report

Quoted By: >>12792084

>>12786998
calling someone a brainlet indicates disagreement with their claims. are you implying that there's a multiplication on L(V,W)?

Linear Algebro

Linear Algebro Thu 04 Mar 2021 14:51:10 No.12788173 Report

Quoted By: >>12790091

>>12786506
what?

Anonymous

Anonymous Thu 04 Mar 2021 15:01:01 No.12788223 Report

Quoted By:

>>12786312
You can't invert determinant zero maps

Anonymous

Anonymous Thu 04 Mar 2021 15:02:52 No.12788228 Report

Quoted By: >>12793773 >>12793937

>>12784235
in finite dimensions there is always a noncanonical one by being gay and picking a basis

Anonymous

Anonymous Thu 04 Mar 2021 22:42:03 No.12790091 Report

Quoted By: >>12790313

>>12788173
if both T and S are in L(V,W), they can't be composed into ST nor TS because the domain and codomain don't agree. therefore there's no multiplication on the set L(V,W).

Linear Algebro

Linear Algebro Thu 04 Mar 2021 23:46:04 No.12790313 Report

Quoted By:

>>12790091
Oh yeah duh

Anonymous

Anonymous Fri 05 Mar 2021 09:43:23 No.12792084 Report

Quoted By:

>>12787202
Brainlet pls

Anonymous

Anonymous Fri 05 Mar 2021 13:30:59 No.12792544 Report

Quoted By: >>12793747

>>12786069
>non-degenerate
what did he mean by this? is it even a word?

Anonymous

Anonymous Fri 05 Mar 2021 19:15:59 No.12793747 Report

Quoted By:

>>12792544
f(u,v) = 0 for all v if and only if u = 0

Anonymous

Anonymous Fri 05 Mar 2021 19:19:30 No.12793764 Report

Quoted By: >>12793779

>>12781344
It is a field though, when V and W are 1-dimensional.

Anonymous

Anonymous Fri 05 Mar 2021 19:20:14 No.12793769 Report

Quoted By:

>>12780550
:]

Anonymous

Anonymous Fri 05 Mar 2021 19:20:39 No.12793773 Report

Quoted By: >>12793780 >>12793785 >>12793792

>>12788228
>gay and picking a basis
Finite dimensional linear algebra IS matrix algebra. Trying to work abstractly without choosing a basis is gay as fuck.

Anonymous

Anonymous Fri 05 Mar 2021 19:21:41 No.12793779 Report

Quoted By:

>>12793764
no, L(V,W) is not a field even if both V and W are 1-dim

Anonymous

Anonymous Fri 05 Mar 2021 19:21:57 No.12793780 Report

Quoted By: >>12794403

>>12793773
lol, engineer detected. You probably learned linear algebra in a numerical analysis course, didn't you?

Anonymous

Anonymous Fri 05 Mar 2021 19:22:32 No.12793784 Report

Quoted By:

>>12780550
What book are you using?

Anonymous

Anonymous Fri 05 Mar 2021 19:22:44 No.12793785 Report

Quoted By: >>12794403

>>12793773
>Trying to work abstractly without choosing a basis is gay as fuck.
kek just look at this brainlet

Anonymous

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Anonymous Fri 05 Mar 2021 19:23:56 No.12793790 Report

Quoted By:

>>12786312

Anonymous

Anonymous Fri 05 Mar 2021 19:24:10 No.12793792 Report

Quoted By: >>12794403

>>12793773
crimge

Anonymous

Anonymous Fri 05 Mar 2021 19:53:26 No.12793937 Report

Quoted By:

>>12788228
Why would you not work in based vector spaces?

Anonymous

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Anonymous Fri 05 Mar 2021 19:53:27 No.12793938 Report

Quoted By:

>>12783554
>people doubted us when we said just throw moar compute lmao at it
WE JUST KEEP MOVING FORWARD, SCALING CHADS

Anonymous

Anonymous Fri 05 Mar 2021 21:20:54 No.12794403 Report

Quoted By: >>12794483

>>12793780
I probably know more maths than you do.
>>12793785
I'm not the one deluding myself that I'm somehow being more clean and pure by not using matrices. Highschooler cope.
>>12793792
You are cringe.

Anonymous

Anonymous Fri 05 Mar 2021 21:36:08 No.12794483 Report

Quoted By:

>>12794403
>I probably know more maths than you do.
dunning-kruger much?

Anonymous

Anonymous Sat 06 Mar 2021 02:43:55 No.12795530 Report

Quoted By:

>>12785755
explain the hard problem of consciousness, dipshit

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