10
Katakompe
10d

# I just cant Wrap my head around matrices and linear Algebra. I am currently doing a uni course about this and need to implement some eigenvalue solvers. I somehow manage to implement the stuff with the help of pseudocode and the internet but I have nö idea conceptually what all these things like norms, eigenvalues, conditioning etc are supposed to tell me and why. How do people handle this so naturally?

• 3
I got it when I started to visualise it.
Jupyter is a great tool for this.
• 0
Nööö
• 2
It’s like arrays of arrays.
• 6
3Blue1Brown channel provides help in conceptual understanding of the subject. Pretty high quality videos https://youtu.be/PFDu9oVAE-g
• 0
Bruh it’s the easiest topic. You just kinda do things in parallel, sometimes just treat basic operations like functions, even more like overridden methods
• 4
@electrineer this. 3blue1brown is awesome, I basically learned calculus from his videos instead of my teacher. I hate how teachers just say "here's the formula, off you go" like no, that's not how it works. You have to understand why and how it works, not just accept stuff as a fact and be done with it.
• 0
Why, that's easy. If an NxN matrix as linear transformation puts some vectors upon themselves, that's the eigenvectors. They can be longer or shorter than originally, and the proportionality factor is the eigenvalue.

If you have a large spread between the eigenvalues, that leads to numerical instability with computer solvers, which is a bad condition.
• 1
Concepts are only easy when they click. If you're struggling with a concept your lecturer provides, you should find other resources that explain it in different ways. 3B1B is very good, khan academy will have the topic as well.
• 0
From the theoretical point of view, it might be easier to start with the theory (and algorithms) of real symmetric matrices or of self-adjoint matrices.

The spectral properties of these are much simpler, and then you can go from there to the fully general case.
• 1
As other people said, look for 3blue1brown's videos.

In my experience many professors and books don't give you the right point of view on this topic. This guy does.