Eigenvalues and Eigenvectors

[@MalcolmAkner]

I learn so much of the math-thinking from this channel. Physics major here, but we all know that physics is just applied maths; this stuff is always at the root of our understandings, it is the basis of our models. Thank you Dr Peyam for doing this, I never lose your train of thought!

[@stevekaszycki8629]

Always dig seeing linear algebra applied to polynomials--it really helps gain a deeper appreciation for the subject beyond merely matrices (though any and all matrix related videos are welcomed).

[@tracyh5751]

looking at the formula, x^2+1 and x are linearly independent eigenvectors with eigenvalue 1. Not sure what the last eigenvalue is though.

[@tracyh5751]

Ah and 1-x^2 is an eigenvector with eigenvalue -1.

[@drpeyam]

Yeah, but how did you find those? And what about harder examples?

[@LeoLokoII]

"So that everything you learned so far is not in vain"

[@virat.chauhan]

Happy Teacher's Day Sir

[@drpeyam]

Thank you!!!

[@pythonanimalia]

@@drpeyam It's only celebrated in India. But happy teachers' day :)

[@haythamhawamdeh6123]

I think I will like this vdu, again, I like ur way. Biggest thanks 😀

[@fnegnilr10]

Have you ever done a list of your favorite "basis math" books?

[@drpeyam]

Yeah, it’s in my interview with bprp

[@HussamJihaz]

and it's orthogonal yaay!

[@54.5mviews3]

Thanks for this

[@sadface7457]

But can you take the determinent

[@gdiehl8801]

Love your videos. However the last couple are very hard to see on my screen. Camera position too far away?

[@drpeyam]

I don’t have many options, unfortunately

[@corydiehl764]

I'm having a hard time getting a good heuristic understanding of what eigen values and eigen vectors allow me to understand about my framework. An analogous example of what I'm looking for: The derivative gives rise to "slope" which yeilds optimizations, related rates, machine learning, local linear approximations to locally solve hard problems and a bunch of other nice results. I guess I'm missing all of the big analysis tools you get from eigen values. It just stops at having a nice basis for me.

[@drpeyam]

Maybe this helps: Eigenvectors and Geometry kzbin.info/www/bejne/qGakoGevlpV4sNU

[@joluju2375]

This helped me : kzbin.info/www/bejne/hnenpmyli6Z4Y8k

[@dhunt6618]

math is for winners! I gen victor!

[@drpeyam]

Hahaha

[@dgrandlapinblanc]

Eigen do it so I can do it. Ah ah ah ! However it's pretty cool and thank you very much. :-)

[@DanielCastro-uy7lu]

There's not much information about triangulation of operators, will you make videos about it? 😁