Eigenvectors and eigenvalues | Chapter 14, Essence of linear algebra

I never really thought of Maths of something fun, but your videos make it so easy and most importantly fun to understand all the concepts and how they are actually closely related to each other. I'm so thankful for your videos and really enjoyed watching all of this and your other series on Analysis etc. You're by far the best math teacher and in my humble opinion a million times better than anyone else on YT. Keep up the great work. Thank you so much!

Nice animations. I like the imagery of a circle stretching into an ellipse. It would be nice to illustrate why only symmetric matrices have real eigenvalues (all stretch and no rotation). You can take anything (even shears) to the 100th power with the Jordan normal form (generalized eigenbasis).

Te ano

I just learned the content of a entire semester in a few videos

As I understand it, the main reason that this is studied is that these vectors then become derivatives

Thanks!

In a transformation, many vectors turn into a vector outside of its span, but sometimes there a vector that when apply the transformation, it still on the span (which mean a line) => Hiệu ứng của matrix transformation trên vecto đó chỉ là nhân dài hoặc rút ngắn vecto đó đi(matrix như một scalar)
Nếu ta tìm được vecto đó thì tất cả những vecto khác trên span(line) của vecto đó đều là EIGEN VECTOR

Thanks for the great video. Could you explain the physical interpretation of imaginary eigenvalues? Which conclusion is correct when our eigenvalues are imaginary: (a) there is no eigenvector or (b) the system has an oscillatory behavior.

I haven't dived deep into the math ocean yet but i'm sure you deserve a lot for these detailed videos.

A = Lamda / Unit in scalar 😂

<3

Still try to visualize how subtraction betwen two tranformation actually work... is there no explanation of that one?

Sir, you are awesome! This is golden!!

We need a video about SVD please

WoW! You deserve a lot more recognition and praise...!