/sci/ - Science & Math

>>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.

>>12780550

Neat, isn't it?

Enjoy learning this stuff anon :D

>>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

>>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?

>>12780550
Literally everything is a vector space/module

>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

>>12783554
Excuse me?

>>12780652
You are never going to make it

>>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.

>>12783730
Not yet anon, not yet.

>>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.

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

>>12780550
mfw no canonical isomorphism between [math]V[/math] and [math]V^*[/math]

>>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.

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

>>12780550
0_o

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

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

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

>>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

>>12786312
there's no multiplication

>>12786490

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

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

>>12786711
dubs of truth

>>12786506
shut up brainlet

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

>>12786506
what?

>>12786312
You can't invert determinant zero maps

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

>>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).

>>12790091
Oh yeah duh

>>12787202
Brainlet pls

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

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

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

>>12780550
:]

>>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.

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

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

>>12780550
What book are you using?

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

>>12786312

>>12793773
crimge

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

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

>>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.

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

>>12785755
explain the hard problem of consciousness, dipshit