Matrix representations in general, if that counts?
Complex numbers, polynomials, the derivative operator, spinors etc. they're all matrices. Numbers are just shorthand labels for certain classes of matrices, fight me.
this post was submitted on 18 May 2025
50 points (96.3% liked)
Ask Lemmy
31715 readers
1962 users here now
A Fediverse community for open-ended, thought provoking questions
Rules: (interactive)
1) Be nice and; have fun
Doxxing, trolling, sealioning, racism, and toxicity are not welcomed in AskLemmy. Remember what your mother said: if you can't say something nice, don't say anything at all. In addition, the site-wide Lemmy.world terms of service also apply here. Please familiarize yourself with them
2) All posts must end with a '?'
This is sort of like Jeopardy. Please phrase all post titles in the form of a proper question ending with ?
3) No spam
Please do not flood the community with nonsense. Actual suspected spammers will be banned on site. No astroturfing.
4) NSFW is okay, within reason
Just remember to tag posts with either a content warning or a [NSFW] tag. Overtly sexual posts are not allowed, please direct them to either !asklemmyafterdark@lemmy.world or !asklemmynsfw@lemmynsfw.com.
NSFW comments should be restricted to posts tagged [NSFW].
5) This is not a support community.
It is not a place for 'how do I?', type questions.
If you have any questions regarding the site itself or would like to report a community, please direct them to Lemmy.world Support or email info@lemmy.world. For other questions check our partnered communities list, or use the search function.
6) No US Politics.
Please don't post about current US Politics. If you need to do this, try !politicaldiscussion@lemmy.world or !askusa@discuss.online
Reminder: The terms of service apply here too.
Partnered Communities:
Logo design credit goes to: tubbadu
founded 2 years ago
MODERATORS
Would you elaborate on the last statement?
I'm just being silly, but I mean that if everything can be represented as a matrix then there's a point of view where things like complex numbers are just "names" of specific matrices and the rules that apply to those "names" are just derived from the relevant matrix operations.
Essentially I'm saying that the normal form is an abstract short hand notation of the matrix representation. The matrices are of course significantly harder and more confusing to work with, but in some cases the richness of that structure is very beautiful and insightful.
(I'm particularly in love with the fact one can derive spinors and their transforms purely from the spacetime/Lorentz transforms. It's a really satisfying exercise and it's some beautiful algebra/group theory.)
Negative zero, comes up in comp sci.
I have a strong relationship to what you get when you divide by zero.
Good ol' NaN
I like writing swear words into the mantissa of NaN numbers
You only get NaN for division by zero if you divide 0 by 0 in IEEE floating point. For X/0 with X ≠ 0, you get sign(X)•Inf.
And for real numbers, X/0 has to be left undefined (for all real X) or else the remaining field axioms would allow you to derive yourself into contradictions. (And this extends to complex numbers too.)
i=sqrt(-1) is nice, but im hoping someone finds a use for the number x where |x| = -1 or some nonsense like that because it looks fun to mess with
Those exist in the split-complex number system which adds the number j, where j^2=1 (but j does not equal 1 or -1). The modulus of j is -1.
j = √-1
This comment was sponsored by EE gang
ε, the base of the dual numbers.
It’s a nonzero hypercomplex number that squares to zero, enabling automatic differentiation.
Came here to say this, but since it's already here, I'll throw in a bonus mind-melting fact: ε itself has no square root in the dual numbers.
As a not good at math person, advanced math sounds hella fake sometimes. Like almost a parody of math. I accept that it's real but part of me will always think it's some inside joke or a secret society cult for the lamest god.
A lot of "advanced" maths comes from asking "What if this was a thing, how would that work? Would it even work?", so you could say there's a deliberate sense of "fake" about it.
Dual numbers come from "What if there was another number that isn't 0 which when multiplied by itself you get 0?"
Basic dual numbers (and complex numbers) are no harder than basic algebra, shallow end of the pool kind of stuff, but then not everyone is comfortable getting in the water in the first place, and that's OK too.
Thank you for the info!
Puts on floaties and a brave face, then advances to the shallow end
What is the value in learning about "What if there was another number that isn't 0 which when multiplied by itself you get 0?"
Are there any practical applications IRL for dual numbers?
Edit: Screw Screw theory. Wikipedia says dual numbers have applications in mechanics and to see Screw Theory. I tried reading about it and my eyes glazed over so quickly. Math so isn't for me lol.
Complex numbers 🤝 Split-complex numbers 🤝 Dual numbers
All super rad.
{j|∧} or ĵ just a base vector
∞
Which one?
So complex or quaternion I imagine? 'i' it is!
√-4 = 2
It's all fun and games until someone loses an i.
i?
Clavdivs?
Meow
Elevendy
I always like seeing π.
Pi is a real number, though. It's irrational, but real.
Pi written out is a real number, yes, I’m referring to the symbol representing Pi. Does that not count?
Nnnnno.
Chaitin's constants.
Not even a number.
They are still real numbers. Specifically uncomputable, normal numbers. Which means their rational expansion contain every natural number.
Oops, I misunderstood what an uncomputable is...
In that case, I would say Infinity-Infinity. This time, it's truly not a number.
Zero
It's the absence of a number and has all manner of interesting edge cases associated with it.
Zero is a real number, but interestingly, it's also a pure imaginary number. It's the only number that's both things at once.
As I said .. lots of edge cases :)
It gets deeper. It's also the same as the 0-k-vector, the 0-k-blade, the 0-multivector, the only number that is its own square besides 1, etc...
There are other idempotent numbers in the split-complex and q-adic (for non-prime q) numbers.
Zero is the absence of a quantity, but it is still a number.