Ask Lemmy
A Fediverse community for open-ended, thought provoking questions
Please don't post about US Politics. If you need to do this, try !politicaldiscussion@lemmy.world
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.
Reminder: The terms of service apply here too.
Partnered Communities:
Logo design credit goes to: tubbadu
view the rest of the comments
I say openly that I'm bad at math because I cannot, even with intense effort, intuit concepts that are laid out as pure mathematical expressions. Why do graphs have eigenvectors? What does that even look like?!
Graphs don't have vectors, spaces do. A space is just an n-dimensional "graph". Vectors written in columns next to each other are matrices. Matrices can describe transformation of space, and if the transformation is linear (straight lines stay straight) there will be some vectors that stay the same (unaffected by the transformation). These are called eigenvectors.
Thanks for the response! Honestly wasn't expecting any. I understand what you're saying as a pure student would, but could you explain what you mean by "a space is a just an n-dimensional graph"?
Would the vertices map to some coordinate in space? Or am I completely misunderstanding.
I misunderstood a little, I assumed a function graph, which could be R^n space. But for the graph-theory-graphs (sets of vertices and edges) it's similar, you can model the graph using adjacency matrix (NxN matrix for a graph of N vertices, where the vertices 'mapped' to a row and column by index. Usually consisting of real numbers representing distance between the "row" and "column" node) and look at it from the linear algebra point of view. That allows to model some characteristics of the graph. But honestly I haven't mixed these two fields of maths much, so I hope what I wrote is somewhat understandable.