Linear Algebra 18e: The Eigenvalue Decomposition and Fibonacci Numbers

[darrenpeck]

You deserve to win an award for undergraduate teaching! Congratulations.

[GSOG]

This lecture drives the point that math is beautiful

[danielvazquez]

I was not prepared for how beautiful this would be

[rk]

Your careful step by step explanation of eigenvectors and eigenvalues and their use, particularly when viewed in the algebraic context of their derivation has really helped me in facilitating their use. Your teaching is invaluable!

[boutiquemaths]

Exquisite! And as usual a brilliant exposition. We are so lucky you made these videos 🤩

[electric_sand]

He walks up to your closed mind, opens the door himself, airs the room, places the ideas in appropriate folders, and quietly leaves.

Thenceforth, it becomes an effort to misunderstand.

[_sephirot]

That was so beautiful! Thank you very much!!!

[ektabansal]

first i get to know about this formula using akra bazzi theorem and now using linear algebra, fibbonacci series is as amazing as your lectures

[samchan]

OMG, this really cleared my puzzle that has been in my mind for many years, I have not realized until just now that linear algebra could be used to solve series problem. Thanks, Dr!

[danv]

This was really a thing of beauty. All that work is starting to pay off!

[mayurkulkarni]

really nice set of lectures! I wonder why so less views!! thank you very much!

[mathematicsplusplus]

Thanks for your wonderful lectures! Your phi symbol looks like the empty set symbol :-) Keep up the great work!

[juliushuizing]

Very enlightening example 🙌🏻. Yet how do we go about choosing the right initial vector to start with?

It seems that if you happen to choose another order for the initial input vector, i.e. instead of transpose([an-1, an]) choose transpose(an, an-1), you consequently have to change the matrix from [[1, 0], [1, 1]] to [[0, 1], [1, 1]]. Yet this is a shear matrix and hence the Eigenvalue decomposition fails...

[TuNguyen-oxlt]

wow, the first time I come up with why we has the formula

[Andygg]

Is there an ETA on the next set of videos?

[anishkelkar]

What is the reason for premultiplying RHS by matrix [1 0] . to extract a_subscript(n) ? Can you justify it ?