Kainui
  • Kainui
Just looking for any and all solutions of this functional equation...
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
chestercat
  • chestercat
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Kainui
  • Kainui
\[f^n(x)=f(x)^n\] To help clear up the notation: \[f^3(x)=f(f(f(x)))\] \[f(x)^3 = f(x)*f(x)*f(x)\]
dan815
  • dan815
1
dan815
  • dan815
hmm im trying to think about matrix transformations

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dan815
  • dan815
is there a transformation where applying the matrix is like a unitary rotation
dan815
  • dan815
and then vector can also be unitary so multiplying by itself will leave it unitary
dan815
  • dan815
and there will be a solution wrt to some n
dan815
  • dan815
|dw:1449634100983:dw|
dan815
  • dan815
|dw:1449634653837:dw|
dan815
  • dan815
yooo xD gimme some hints
Kainui
  • Kainui
Hmmm Well I dunno what you're doing haha but I did find several solutions and some of mine look like yours
ganeshie8
  • ganeshie8
.
Kainui
  • Kainui
Like I think you see the infinitely many complex constant unitary or w/e solutions you do, for example: \[f(x)=i\] is a solution to \(f^5(x)=f(x)^5\), \(f^9(x)=f(x)^9\), etc... I also found some other one that works too, by plugging in \[f(x)=x^a\] and solving for a in terms of n, but that's still particular special cases. I would really like some single non constant f(x) that works for all n.
dan815
  • dan815
yeah i know what u mean
dan815
  • dan815
i think there is such a function
dan815
  • dan815
basically like lets find somme unitary matrix solutiosn then we will find eigen values of those matrices and get quadratics form of that to generate our functiosn bruh1
Kainui
  • Kainui
I don't get that idea, like what do you mean?
Kainui
  • Kainui
like can you solve \(f^2(x)=f(x)^2\) as an example with matrices to show me
dan815
  • dan815
okay like u know how all polynomial functions can be turned into matrix represented function
dan815
  • dan815
like for example 2x^2+xy+y^2=0 can be represented in matrix form
Kainui
  • Kainui
Ok yeah go on
dan815
  • dan815
|dw:1449635364161:dw|
dan815
  • dan815
now i was suggesnting we look for something in the eigen values of this matrix in the middle
dan815
  • dan815
then we will have some diagonailzed form and stuff
Kainui
  • Kainui
sure but how does this relate?
dan815
  • dan815
well okay like umm
Kainui
  • Kainui
I am familiar with all this sorta stuff you've said, another fun fact about symmetric matrices is unique eigenvalues of a symmetric matrix have orthogonal eigenvectors.
Kainui
  • Kainui
might be useful to us once we figure out how this connects to our problem I guess
dan815
  • dan815
oh yaa i saw something like this before
dan815
  • dan815
i forget the proof
Kainui
  • Kainui
It's pretty fun, not too complicate
dan815
  • dan815
|dw:1449635780007:dw|
dan815
  • dan815
|dw:1449635867198:dw|
dan815
  • dan815
|dw:1449635981408:dw|
dan815
  • dan815
|dw:1449636097991:dw|
Kainui
  • Kainui
let's say matrix A has these two unique eigenvalues a and b with eigenvectors x and y respectively. Show that \(x \cdot y = 0\) (they're orthogonal) Ax=ax Ay=by Ok so you take these true statements, and we can left multiply by the other vector like this on both: \[y^T Ax = a y^Tx\]\[x^T A y = b x^Ty\] Transpose one of them, they're equal, so the rest follows cause \(a \ne b\) \[\huge \square\]
dan815
  • dan815
what do you mean transpose one of them
dan815
  • dan815
|dw:1449636248477:dw|
dan815
  • dan815
|dw:1449636293324:dw|
Kainui
  • Kainui
Yeah
dan815
  • dan815
|dw:1449636363892:dw|
dan815
  • dan815
|dw:1449636463431:dw|
dan815
  • dan815
|dw:1449636480790:dw|
dan815
  • dan815
i see this means that the only possibility of these 2 expression equaling each other would mean the dot product of x and y are orthogonal
dan815
  • dan815
:)
dan815
  • dan815
beautiful baby
dan815
  • dan815
I AM A BEAUTIFUL BABY
Kainui
  • Kainui
http://static.guim.co.uk/sys-images/Guardian/Pix/pictures/2012/10/17/1350479348659/Crying-baby-013.jpg
dan815
  • dan815
hahahaHAAHHAhahahaAHAHHAHA
dan815
  • dan815
U R SO FUNNNY
Kainui
  • Kainui
lol calm down
dan815
  • dan815
hshshshsahahah
Kainui
  • Kainui
YOU ARE OUTTA CONTROL!!!
dan815
  • dan815
HAHAHa please delete all my msg that are compromising
dan815
  • dan815
i am leaving you to it boss
Kainui
  • Kainui
Hahaha what
Kainui
  • Kainui
I'm not your post-janitor
dan815
  • dan815
please editor!! think about it like editor
dan815
  • dan815
You be the guy that decides on what comments of mine we should make public
Kainui
  • Kainui
clean up ur mess or I put u in time out. There's a reason moms = mods
dan815
  • dan815
To bring up the image of your client
dan815
  • dan815
YO NEXT question man next question!
dan815
  • dan815
lemme catch up to your math knowledge a little teach me some new stuff
Kainui
  • Kainui
lol idk what's to teach, tensors? I leave the country on saturday man
dan815
  • dan815
LOLOLOl
dan815
  • dan815
bruh pls plsplspls
Kainui
  • Kainui
I'm busy chillin doing w/e I feel like
dan815
  • dan815
BRUH PLEASE!
Kainui
  • Kainui
I am doing some programming right now
Kainui
  • Kainui
and been doing some number theory nothing too serious
dan815
  • dan815
okay lets do it! tell me what to make
dan815
  • dan815
ill have it done for u rn
dan815
  • dan815
okay whatever just gimme a prolem quickl man i need it bad i need it
dan815
  • dan815
I NEED IT RIGHT NOW OMGGG
Kainui
  • Kainui
hmmm uhhh ok teach daggie
dan815
  • dan815
LOOOOL
dan815
  • dan815
LOLOLOLOLOLOLOLOLL
Kainui
  • Kainui
daggie is really smart and has a larger attention span than you, she'll easily pass you up
dan815
  • dan815
does daggie get this eigen value stuff
Kainui
  • Kainui
she's reading this right now, not kidding didn't I show you that organic chemistry thing we did the other night?
dan815
  • dan815
BRO how can u say that
dan815
  • dan815
From now on iam back to math!
Kainui
  • Kainui
Do you get this eigen stuff? Teach her matrices
dan815
  • dan815
BRO but i just got back after a 6 month break
Kainui
  • Kainui
hahaha ok
dan815
  • dan815
NO i dont have time for such noobs
dan815
  • dan815
loool!
dan815
  • dan815
let the noob learn herself
Kainui
  • Kainui
I know but like I'll be gone for a month
dan815
  • dan815
watch us and learn
dan815
  • dan815
watch how the masters do it
dan815
  • dan815
if its a question that interests me it will be solved
dan815
  • dan815
simple as that
Kainui
  • Kainui
wowwwww
dan815
  • dan815
:)
Kainui
  • Kainui
I'm reporting you to preetha ur no longer a qualified helper u hear me?
dan815
  • dan815
OMG please dont stop okay im sorry dude
Kainui
  • Kainui
lolol xD
dan815
  • dan815
LOL STOP IT
Kainui
  • Kainui
no more owl bucks how will u pay rent?
dan815
  • dan815
LOOOL shush
dan815
  • dan815
yo next question dude please!
Kainui
  • Kainui
Ok so dan you know how you said this stuff about
Kainui
  • Kainui
like "solving OS"
Kainui
  • Kainui
maybe we should solve PA instead
dan815
  • dan815
um ya sure go on
dan815
  • dan815
okay lets do it right now
dan815
  • dan815
What do u want to solve?
Kainui
  • Kainui
since all they ask for is answers I mean we could just make like a PA bot
dan815
  • dan815
okay how about we start with something simple
dan815
  • dan815
like gathering data
dan815
  • dan815
from a paragraph
dan815
  • dan815
and fill out a form for us
Kainui
  • Kainui
idk, also my friend has this problem with code where he works with a bunch of drunk programmers or something that can't type well so he wants a program to parse drunk speech and if an instant message contains a certain garbled keyword or something, it will save that message.
dan815
  • dan815
a form saying Length of the question in words : Number of times slope appears : Number of times _____ appears: .... Number of digits in text: Number of groups of digits separated by spaces: and so on: Design it so that we have a easy way of implementing new tasks for it to do a find for, and also possibly a way of removing methods, or maybe just not using the methods for later on
Kainui
  • Kainui
ok dan how about we solve an unsolved problem instead like something simple like prove there are infinitely many twin primes, the collatz conjecture, goldbach conjecture, or riemann hypothesis
dan815
  • dan815
yo bro i feel like i solved this right now!
dan815
  • dan815
This is all we need yo
dan815
  • dan815
It will be so sick listen to me man
dan815
  • dan815
There will be 3 other things we we will keep track of for the seach methods
Kainui
  • Kainui
I hear you but the implementation of this code will be boring
dan815
  • dan815
But dude we will not just be making a code here
Kainui
  • Kainui
it always starts out simple until you get into it and realize you're in a tangled web of garbage I've been down this path
dan815
  • dan815
we are making a searching algorithm
dan815
  • dan815
dude its all about designing an efficient searching algorithm
dan815
  • dan815
why cant you see this bruh!! thats where the difficulty is
Kainui
  • Kainui
ok go on, sounds like rule based expert system. I've been watching through some algorithm design stuff for making artificial intelligence programs from MIT OCW
Kainui
  • Kainui
Maybe we should look at that and try to improve those
dan815
  • dan815
u wanna start with someones code and project already?
dan815
  • dan815
I thought we should try our own hand at making a searching program
Kainui
  • Kainui
sure, I don't care just as long as you pick something that'll be interesting enough until the end of the week
dan815
  • dan815
okay :)
dan815
  • dan815
lets do thsi then!!
Kainui
  • Kainui
I'm gonna heat up some coffee and brb, choose something and let's move into some other thing that's less laggy
dan815
  • dan815
omg i am thinking of the craziest stuff yoo!!
dan815
  • dan815
YO MAN OMG!
dan815
  • dan815
i know how to program dictionaries BRO
Kainui
  • Kainui
HAhaha wat
dan815
  • dan815
:)
dan815
  • dan815
u really wanna see?
Kainui
  • Kainui
alright message me on skype sure
dan815
  • dan815
okay :)

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