Matrix with respect to a basis

Calculating the matrix of A with respect to a basis B, and showing the relationship with diagonalization. Finding a basis B such that A is diagonal

[Ensivion]

If you have a transformation expressed in its eigenbasis, it's diagonal with the eigenvalues on the diagonal, which is obvious since you get a scalar multiple of your eigenvectors when you operate on the eigenvectors with the matrix associated with those eigenvectors. It's the definition of eigenvectors. This could be a video to watch along with 3Blue1Brown's essence of Linear Algebra.

[yeyuan]

very helpful. I have been struggling with this problem for a long time. I watched a lot of videos but this is the first time I truly understood! Thank you a lot!

[shaesiegert]

I love your videos. They are so helpful to me! Thank you for the great teaching!

[supramayro]

Bless you God Dr.Peyman. Your videos are essential for student like me and they help ALOT

[HasXXXInCrocs]

Yay! This is exactly what I'm learning in class now! Just in time for my next exam! Thanks Dr.P :)

[sebsmith]

Your linear algebra lectures have really helped me understand how to do my uni assignments, thanks a lot! :))

[ankurmazumder]

Hello sir, a really nice explanation. Would it be possible to cover topics on probability and combinatorics? I really love your work. Thank you

[lambdamax]

The Oracle told me I could find Neo in this Matrix transformation

[bbk]

your pens are really nice mate they standout a lot :)
lots of love from UCL
PS I wasn't paying attention

[namansingh]

Thanks i just have exam i finally understood this topic now😂👌thank💕

[paololarocca]

C.with the second method, if pb is a square matrix, can i use Cramer theorem?

[liangtong]

The best Math prof. you always being so clear, thank you

[Chester]

Thank you for guiding us through the wonderful world of matrices :-)

[jonasdaverio]

I think many people are gonna have fun commenting first