/sci/ - Science & Math » Thread #11476814

6KiB, 574x154, CodeCogsEqn.png

View Same Google iqdb SauceNAO

Exponential of a vector

Anonymous Tue 17 Mar 12:27:00 2020 No.11476814 View Reply Original Report

Quoted By: >>11476898 >>11477362 >>11477447 >>11477481 >>11477524 >>11478972

Does this have any use?

Anonymous

Anonymous Tue 17 Mar 2020 13:01:15 No.11476844 Report

Quoted By: >>11476959 >>11477273

Math doesn't evolve based on how useful it will be. (obviously, there are exceptions, like calculus)
Eventually, use if found for the most part of what is discovered in math when some scientist or engineer realize some mathematical concept is just what he needs to model something.

Anonymous

Anonymous Tue 17 Mar 2020 13:33:27 No.11476898 Report

Quoted By: >>11478926

>>11476814
Simulations and shit. Crypto maybe?

Anonymous

Anonymous Tue 17 Mar 2020 14:03:50 No.11476959 Report

Quoted By:

>>11476844
For most of history, math evolved by usefulness. Pure math memes are only recent.

Anonymous

Anonymous Tue 17 Mar 2020 16:43:18 No.11477273 Report

Quoted By:

>>11476844
really? Then why is the reaction of literally every choicefag something along the lines of
>but muh calculus
>but muh differential equations
>how are you going to do that finitists
then they run away never listening to the answers

Anonymous

Anonymous Tue 17 Mar 2020 17:18:33 No.11477362 Report

Quoted By: >>11480241

>>11476814
>1+r
kys

Anonymous

Anonymous Tue 17 Mar 2020 17:47:09 No.11477447 Report

Quoted By:

>>11476814
Bro you're adding a scalar to a vector.

Anonymous

Anonymous Tue 17 Mar 2020 17:59:12 No.11477481 Report

Quoted By:

>>11476814
your vector space should be a banach-algebra or something, or else this doesn't make sense

Anonymous

View Same Google iqdb SauceNAO Bildschirmfoto 2020-03-17 um 19. (...).png, 341KiB, 2072x992

Anonymous Tue 17 Mar 2020 18:14:25 No.11477524 Report

Quoted By: >>11480258

>>11476814
incidentally already wrote about it on /mg/ yesterday
>>11473074
Ihe bottom example in pic related is a special case.

Helps if you e.g. use multiples of Pauli matrices as base for your r-vector

Anonymous

Anonymous Wed 18 Mar 2020 02:51:19 No.11478926 Report

Quoted By:

>>11476898

Yep pretty much, machine learning and finance

You can use the lehmann scheffe theorem to find UMVUE statistics which you can put in a cramer rao based machine learner using RMSE. Or you can work with stochastic discount forces using partial difussions which probably will reduce to some kind of vector exponential expression.

Anonymous

Anonymous Wed 18 Mar 2020 03:11:18 No.11478972 Report

Quoted By: >>11480086

>>11476814
Adding a scalar and a vector?

Anonymous

Anonymous Wed 18 Mar 2020 13:47:35 No.11480086 Report

Quoted By: >>11480115

>>11478972

No stranger than adding reals and imaginaries. If it's useful then use it.

Anonymous

Anonymous Wed 18 Mar 2020 14:04:06 No.11480115 Report

Quoted By:

>>11480086
Because there isn't a natural way to define it otherwise surely then exp : V -> V * R if V is your vector space. How useful could that map be?

El Arcón

View Same Google iqdb SauceNAO TIMESAND___7vjnbndnmmss2m28zzlpk (...).png, 8KiB, 827x89

El Arcón Wed 18 Mar 2020 14:58:50 No.11480200 Report

Quoted By: >>11480217

If you choose to take
$\vec r\cdot\vec r=r^2~~,$

then $e^{\vec r}$ has plenty of meaning.

Anonymous

Anonymous Wed 18 Mar 2020 15:07:21 No.11480217 Report

Quoted By:

>>11480200
This is used to solve many diff. equations

Anonymous

Anonymous Wed 18 Mar 2020 15:18:55 No.11480241 Report

Quoted By:

>>11477362
This.

And yes, it has applications for example in electrodynamics.

Anonymous

Anonymous Wed 18 Mar 2020 15:26:02 No.11480258 Report

Quoted By:

>>11477524
>Since j^2 = 1
I...what? So now 1 has four roots, and -1 has none?

Anonymous

Anonymous Wed 18 Mar 2020 15:31:06 No.11480269 Report

Quoted By:

The reason why Euler's identity is useful is because you can exploit the properties of exponents (that when multiplied, the powers add for example) when it's in exponential form. This is very useful when working with integrals and algebra as you might imagine.

So do the properties of exponents hold true in this case?

Capcode	All Only User Posts Only Moderator Posts Only Admin Posts Only Developer Posts
Show Posts	All Only With Images Only Without Images
Deleted Posts	All Only Deleted Posts Only Non-Deleted Posts
Ghost Posts	All Only Ghost Posts Only Non-Ghost Posts
Post Type	All Only Sticky Threads Only Opening Posts Only Reply Posts
Results	All Grouped By Threads
Order	Latest Posts First Oldest Posts First

Your latest searches