/sci/ - Science & Math

>>12089176
I'm absolutely certain there are such theorems.
Especially since e.g. eigenvalues of random matrices and stuff like that are well studied.
If I can guess behind your motivations, note that a good way to deal with noise on symmetric matrices is to work with their roots, e.g.
https://en.wikipedia.org/wiki/Kalman_filter#Square_root_form

>>12048569
I think it was a short hype in the 80's but it didn't catch on. I suppose because the formalism can be modeled okay enough with straight forward probability theory and people don't like learning new framework where the scope of applications isn't so clear.

>>11933006
>thoughts on the godel incompleteness theorem?

>there are computationally undecidable statement in arithmetic
Since we have computers now and the Halting problem result is not too hard to understand, today Gödel 1 doesn't really have the same impact on people. It's been absorbed into common knowledge to a good degree.

>arithmetic can't formalize it's consistency
It's somewhat superseded by Tarski's result and there's several proves of consistency of Peano arithmetic in other systems (Gentzens ordinals, modal operators in provability logic with alternative formalizations of Con_T, self-consistent arithmetic-like theories with infinite axiom systems, and weak self-consistent-proving arithmetics if you want to count them too). Gödel 2 is thus somewhat of a party trick and no more, imho.

>>11933006
>I've always had this hunch it may be the solution to unsolved mathematical problems such as the millennium prize problems
A Riemann hypothesis disprove is arithmetical (RH is Pi_1 I think) and some of the Millenium Problems like Navier Stokes existence-uniqueness are pure math memes to begin with anyway.
There's academic papers on potential undecidability of PvNP if you're interested.

>>11920769
Women in STEM are smarter than average, but usually they are way too full of themselves. I'd rather coom inside a chess qt :3

>>11894321
Better?

>>11893621
I think of it because I played with it two years ago.
Take any active trading platform, put 100$ there, figure out the Python API (currency of choice => price, buy-order, sell-order) and query the price once a minute. You get a stream of prices and the algorithm when to buy and when to sell is really up to you.
The most naive way to make money is to do this on two exchanges and buy+sell whenever the price difference on the two is larger than the trading fee the exchange charges. Obviously, you need two exchanges with lots of volume and obviously, don't expect to make any money because if you find this situation, clearly other people are already doing it.

I ended up never making a nice summary about my hacky bot, but you'll definitely find youtubers or tutorials about it.
For something arguably related, I'm currently thinking if I should try to write a chess-bot from scratch and use lichess.org as interface. I had some fun with the NIST dataset and a rough idea of how chess programming works and I'd like to combine the two. I do C++ and Python at work too, and I even know rudimentary Haskell - although I'd say Python is the obvious choice for quickly doing the website interaction. If you're interested in something like that (or somebody else, for that matter), you can find my contacts somewhere on the user page here
https://youtu.be/z2aq21lMw40
https://youtu.be/YdKVqfKbXxg

Is there any way to find a series expansion for
[math] \dfrac{1}{1-z} [/math]
of the form
[math] \sum_{k=0}^\infty a_k z^k [/math],

converging on some patch outside of the unit disk in the complex numbers?

Emphasis on all k being in {0,1,2,...} and not negative.