Eigenvectors and Generalized Eigenspaces

A video about the nice geometric intuitions behind eigenvectors and eigenvalues, and their generalized counterparts, generalized eigenvectors and generalized eigenvalues.
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[@une4s]

I got here from the link in the Coursera course, and this video has been super helpful in understanding some of that material better. Honestly, I found the way you explain it here much easier to follow, and the visuals are really clear.

[@robharwood3538]

This was sooo helpful, giving me a lot of new insights that had stumped me for a long time. Thank you, Luis!

[@jakob3267]

Your explanation of generalized eigenvectors were super clear and easy to understand. Know i finally get it. Thank you!

[@pakistan3965]

The way you explain things is fabulous. You're one of the best mentor i ever had. I respect you alot and love you. More success to you sir! ❤❤

[@SerranoAcademy]

Thank you so much! It's an honour to be part of your learning journey. Sending lots of love, and all the best to you!

[@MyAows]

As always, wonderful explanation, Luis.

[@sumathiravi9914]

Really that is an amazing video. Kindly do keep up the good work Luis sir.

[@NoNTr1v1aL]

Absolutely amazing video!

[@jimlbeaver]

I had never heard of this before…thanks for the clear explanation

[@prof.nevarez2656]

Hi Luis! Awesome visualization and explanation of such a cornerstone topic in Linear Algebra! I am teaching Linear Algebra and will definitely use this as a resource for my students. I met you at a Latinos in the Mathematical Sciences Conference at IPAM back in 2015 I believe, fellow UMich grad, Go Blue! I remember that you were working at RUclips back then. And you also worked with Alexis Cook at some point, Go Blue again! Anyways, it's cool to follow your journey and I, as many others, benefit greatly from your insights that you have in your content. Looking forward to the next one!

[@SerranoAcademy]

Thank you! It's great seeing you over here again, and thanks for using the video for your class! Hope to see you some time in the future, and go blue!! :)

[@chandamwenechanya8614]

Thank you Luis. This is very insightful.

[@skgamers2993]

This is what i was looking for after completing your coursera course.

[@rishavdhariwal4782]

can you tell me the couse name?

[@tandavme]

Thank you for great videos, Luis !

[@VidyaBhandary]

Thank you so much !! This is a clear explanation.

[@tuckerantell8449]

EXCELLENT visuals thank you!

[@jorovifi89]

high quality content. thank you

[@statatease7661]

Good presentation. Thank you.

[@darkseid856]

What an amazing video . 👌👍

[@felipesants8936]

GREAT LECTURE

[@lakshman587]

Thanks for the video!!!

[@mikeczyz]

as usual, great video.

[@aitanapalomanespardos7089]

14:21 could you make a video, or give some intuition as to why the generalised eigenvector needs to have the same eigenvalue as the eigenvector? Lovely video, I enjoyed the geometric visualisation.

[@muhittinselcukgoksu1327]

Super.Thank you soo much...

[@herumbshandilya9046]

Just the thing that this world needed🙌

[@SerranoAcademy]

Thank you Herumb!

[@wencolega1991]

Desde España, increíble!! 😀

[@kellermarquardt6519]

You are fantastic

[@shravan6457]

@serranoacademy in case you would like to edit the Video with a comment, at 7:38, you inadvertently mentioned Eigen Values for Eigen Vectors and then Eigen Vectors for Eigen Values.

[@SerranoAcademy]

Oh thank you! Hard to make the edit, but I'll add a comment.

[@anelm.5127]

Amazing.. Particle Filter for Localization would be much appreciated

[@ssshukla26]

Without seeing the video I have already liked it. Am waiting for your book to be released since start of 2021 (the one which you writing with Manning publication). So can you tell the RUclips community when it will be released? It has delayed so many times that I had give up on keeping track of it...😓

[@SerranoAcademy]

Thanks Sunny! and thanks so much for your patience with the book. Just earlier today I submitted the final version, so it'll be published very soon!

[@ssshukla26]

@@SerranoAcademy Great. Congratulations. Thanks again for the content and the book.

[@ThinAirElon]

same here ! I orderd MEAP version. I wish I could have teacher like this in my school/college days !

[@kr4T0X]

if both Eigenvalues are same, say 2 and 2, then all lines are sent to themselves. So, are there now infinite eigenspaces?

[@SerranoAcademy]

Great question! Two things can happen, if you have a generalized eigenspace, like in the example, OR, if the matrix is 2 times the identity matrix, in which case every vector gets sent to twice the vector, which means every vector is an eigenvector.

[@wesleysuen4140]

😘