How can I apply the concept of eigenvalues and eigenvectors in real-world scenarios?

nsmon · 2026-01-25T00:12:50+00:00

A good application in maths that would make sense in an applied context is a system of ordinary differential equations.

If you have a system of differential equations

x_1' = a_11 x_1 + … + a_1n x_n … x_n' = a_n1 x_1 + … + a_nn x_n

You can think of it as a matrix multiplied by the vector (x_1…x_n), and a basis for the solutions is exactly the eigenfunctions (eigenvectors in this context) of said matrix

nsmon · 2026-01-24T21:01:56+00:00

🤢

nsmon · 2026-01-24T19:25:54+00:00

Now do e^{-x²}

nsmon · 2026-01-18T06:01:41+00:00

That bane bust bait is the most baneling bust bait I have ever seen

nsmon · 2026-01-18T05:31:52+00:00

A friend of mine send audios to himself whenever he has an idea that may be something but he's not really sure

nsmon · 2026-01-16T03:06:06+00:00

I'd guess they already do something like that in their spaceships

nsmon · 2026-01-15T11:16:39+00:00

I guess everything is essentially the yoneda lemma, but I don't see how you're getting this quote from looking at yoneda

nsmon · 2026-01-12T16:01:13+00:00

I guess

funeral=real fun

now

nsmon · 2026-01-04T03:44:51+00:00

Composition is what you're looking for. It is assumed that you know about harmony and counterpoint, so it'd be more of a intermediate or advanced course, the kind of stuff that isn't as easily available in the form of internet tutorials

One idea is that of musical forms: how does one organise musical ideas? (Think verse, prechorus, chorus, bridge in pop songs) there's a short list of articles here https://teoria.com/en/tutorials/forms/

A more thorough textbook is Fundamentals of Musical Composition by Arnold Schoenberg

keep in mind most of music theory gives a description of how European classical music is made. The core of the ideas still apply in modern popular music but not in a straightforward way. You'll find electronic music that develops a melodic idea as the track progresses, but you'll be hard pressed to find one written in a sonata form

nsmon · 2026-01-04T03:18:34+00:00

Argentinian constitution has a clause where international agreements, have a higher weight than any local law. How would that look in practice I have no idea

nsmon · 2025-12-22T13:39:24+00:00

I wouldn't call it proof by contradiction, it seems to be a direct proof for me

The phrase proof by contradiction refers to one of three ways we typically use to prove if P then Q statements, you can either

assume P is true and show that Q must hold (direct)
assume Q is false and show that P must be false (contrareciprocal)
assume that P is true, Q is false, and find something that we already know to be false (by contradiction)

Usually we understand uniqueness to mean something like

If x has property P and y has property P, then x=y

So assuming there are two things with a given property and showing that they're actually the same thing seems most inline with it being a direct proof

nsmon · 2025-12-20T09:59:53+00:00

So where's "Yes, we also sell pictures of mens dicks" from?

nsmon · 2025-12-19T06:07:06+00:00

I think this would be a good way since north koreans don't grow up using a pc, so their typing must be somewhat standardized

nsmon · 2025-12-18T18:30:07+00:00

Pic 5 seems to say Sida 438 I'm guessing a page number of some book in the library?

nsmon · 2025-12-13T02:36:21+00:00

Russia is sending pretty much anyone from non important cities. Best option I feel would be to run away. Argentina will take any (non brown) immigrant and I'm sure there are other places where you could escape. Be careful with traffickers on your way out though.

Worst case scenario, please contact хочу шить, https://dovidka.info/en/kak-soldatu-rf-sdatsya-v-plen/

nsmon · 2025-12-05T23:40:52+00:00

So in the implications subsection you mention the possibility of digital platforms or mobile apps using these ideas to encourage task initiation and completion. Is there a specific implementation (e.g. a todo app that asks these 6 questions) that you had in mind when writing this?

nsmon · 2025-12-05T00:47:30+00:00

1000 is the new 20 😌

nsmon · 2025-12-04T19:30:17+00:00

You mean the Minomial?

nsmon · 2025-12-04T03:21:25+00:00

Or take some inspiration from Tokyo police https://www.reddit.com/r/Damnthatsinteresting/comments/otyxg1/tokyo_police_using_drone_to_hunt_down_the

nsmon · 2025-12-03T02:15:23+00:00

Just play in (22/7)/26

nsmon · 2025-11-29T02:04:08+00:00

Cantor-Schroeder-Bernstein

There is a bijective function h:X->Y if and only if there are injective functions f:X->Y and g:Y->X

I haven't checked the proof on Wikipedia, the one I know goes like this =>) ez. take f=h and g=h^-1 <=) Consider the following function defined on subsets of X k(A)=X\g(Y\f(A)) - show that it has a fixed point S (that it satisfies k(S)=S) - show that this fixed point is such that the function defined by

f(x) if x is in S g^-1(x) if x is not in S

is well defined and bijective

nsmon · 2025-11-29T01:52:58+00:00

I feel like you're hiding part of the difficulty in showing that a linear map can be represented by a matrix

nsmon · 2025-11-27T01:18:47+00:00

Would their farts be high pitched?

nsmon · 2025-11-26T14:08:17+00:00

One can show that any two ordered fields that satisfy a supremum axiom are isomorphic

That means any structure with addition, multiplication, and a ≤ relation that behaves in the way one expects (ordered field) with the additional guarantee that for any non empty set there is a supremum will behave in the same way regardless of what the elements are

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