Linear Algebra 18e: The Eigenvalue Decomposition and Fibonacci Numbers

[@MathTheBeautiful]

Go to LEM.MA/LA for videos, exercises, and to ask us questions directly.

[@darrenpeck156]

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

[@MathTheBeautiful]

Thank you! Comments like yours are all the reward I need!

[@r2k314]

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!

[@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.

[@boutiquemaths]

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

[@MathTheBeautiful]

Thank you, it means a lot!

[@samchan2535]

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!

[@danielvazquez8966]

I was not prepared for how beautiful this would be

[@MathTheBeautiful]

I felt the same way when I first saw it.

[@GSOG2]

This lecture drives the point that math is beautiful

[@danv8718]

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

[@ektabansal5332]

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

[@OtterMorrisDance]

Wonderful video !

[@_sephirot47]

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

[@MathTheBeautiful]

Thank you for letting me know that you liked it!

[@taotaotan5671]

Mind-blowing. Thank you.

[@mayurkulkarni755]

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

[@MathTheBeautiful]

Fewer views, more memories!

[@Andyg2g]

Is there an ETA on the next set of videos?

[@mathematicsplusplus]

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

[@juliushuizing1683]

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...

[@anishkelkar6434]

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

[@MathTheBeautiful]

Yes, just to extract the first of the two entries in a column.

[@vijaybsemwal]

Very interesting video

[@TuNguyen-ox5lt]

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

[@cardinalblues7121]

this is amazing

[@MathTheBeautiful]

Yes, very elegant!