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\[f^n(x)=f(x)^n\] To help clear up the notation: \[f^3(x)=f(f(f(x)))\] \[f(x)^3 = f(x)*f(x)*f(x)\]
hmm im trying to think about matrix transformations
is there a transformation where applying the matrix is like a unitary rotation
and then vector can also be unitary so multiplying by itself will leave it unitary
and there will be a solution wrt to some n
yooo xD gimme some hints
Hmmm Well I dunno what you're doing haha but I did find several solutions and some of mine look like yours
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.
yeah i know what u mean
i think there is such a function
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
I don't get that idea, like what do you mean?
like can you solve \(f^2(x)=f(x)^2\) as an example with matrices to show me
okay like u know how all polynomial functions can be turned into matrix represented function
like for example 2x^2+xy+y^2=0 can be represented in matrix form
Ok yeah go on
now i was suggesnting we look for something in the eigen values of this matrix in the middle
then we will have some diagonailzed form and stuff
sure but how does this relate?
well okay like umm
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.
might be useful to us once we figure out how this connects to our problem I guess
oh yaa i saw something like this before
i forget the proof
It's pretty fun, not too complicate
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 \(a \ne b\) \[\huge \square\]
what do you mean transpose one of them
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
I AM A BEAUTIFUL BABY
U R SO FUNNNY
lol calm down
YOU ARE OUTTA CONTROL!!!
HAHAHa please delete all my msg that are compromising
i am leaving you to it boss
I'm not your post-janitor
please editor!! think about it like editor
You be the guy that decides on what comments of mine we should make public
clean up ur mess or I put u in time out. There's a reason moms = mods
To bring up the image of your client
YO NEXT question man next question!
lemme catch up to your math knowledge a little teach me some new stuff
lol idk what's to teach, tensors? I leave the country on saturday man
bruh pls plsplspls
I'm busy chillin doing w/e I feel like
I am doing some programming right now
and been doing some number theory nothing too serious
okay lets do it! tell me what to make
ill have it done for u rn
okay whatever just gimme a prolem quickl man i need it bad i need it
I NEED IT RIGHT NOW OMGGG
hmmm uhhh ok teach daggie
daggie is really smart and has a larger attention span than you, she'll easily pass you up
does daggie get this eigen value stuff
she's reading this right now, not kidding didn't I show you that organic chemistry thing we did the other night?
BRO how can u say that
From now on iam back to math!
Do you get this eigen stuff? Teach her matrices
BRO but i just got back after a 6 month break
NO i dont have time for such noobs
let the noob learn herself
I know but like I'll be gone for a month
watch us and learn
watch how the masters do it
if its a question that interests me it will be solved
simple as that
I'm reporting you to preetha ur no longer a qualified helper u hear me?
OMG please dont stop okay im sorry dude
LOL STOP IT
no more owl bucks how will u pay rent?
yo next question dude please!
Ok so dan you know how you said this stuff about
like "solving OS"
maybe we should solve PA instead
um ya sure go on
okay lets do it right now
What do u want to solve?
since all they ask for is answers I mean we could just make like a PA bot
okay how about we start with something simple
like gathering data
from a paragraph
and fill out a form for us
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.
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
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
yo bro i feel like i solved this right now!
This is all we need yo
It will be so sick listen to me man
There will be 3 other things we we will keep track of for the seach methods
I hear you but the implementation of this code will be boring
But dude we will not just be making a code here
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
we are making a searching algorithm
dude its all about designing an efficient searching algorithm
why cant you see this bruh!! thats where the difficulty is
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
Maybe we should look at that and try to improve those
u wanna start with someones code and project already?
I thought we should try our own hand at making a searching program
sure, I don't care just as long as you pick something that'll be interesting enough until the end of the week
lets do thsi then!!
I'm gonna heat up some coffee and brb, choose something and let's move into some other thing that's less laggy
omg i am thinking of the craziest stuff yoo!!
YO MAN OMG!
i know how to program dictionaries BRO
u really wanna see?
alright message me on skype sure