Jordan Normal Form 2 | An Example

[@KogularajK.]

What makes your videos outstanding is that your choice to use nontrivial examples and more importantly nontrivial matrix dimensions.. I just love it..

[@brightsideofmaths]

Thank you very much :)

[@zachchairez4568]

You are honestly one of the greatest mathematicians on KZbin. You are helping me so much in my graduate career. I loved your videos on Lebesgue Measure. Keep doing you!

[@PunmasterSTP]

How has your academic career been going?

[@willadem8643]

This has to be the stupidest comment in the history of KZbin. "Greatest Mathematicians on KZbin" - Yeah math is about formulas and not about intuition. Dude goes through the entire video without one mention of what eigenvalues or eigenvectors actually are. In his other video about geometric and algebraic multiplicity, same story, literally like all fucking other math teachers.

[@zachchairez4568]

@@willadem8643Are you ok?

[@zachchairez4568]

@@PunmasterSTPPh.D. will be done in August, thanks for asking! 😁✌️

[@PunmasterSTP]

@@zachchairez4568 Awesome; I'm glad to hear it!

[@alainmifsud3968]

Your'e the best mathematics education channel on youtube and better than most universities hands down

[@brightsideofmaths]

Wow. Thank you very much :)

[@lume.3887]

This is taught so well. At my university they teach us what the JNF is and then leave it to us to work out all the possibilities for each jordan form in the exam.

[@brightsideofmaths]

Thanks! I hope this here helps your for your exams :)

[@lucyferyx]

This was very well drawn and explained, thank you so much!

[@brightsideofmaths]

You're very welcome!

[@VaibhavKumar-zh5yu]

Thank you so much for these videos. You are a blessing!

[@brightsideofmaths]

Thank you very much :) And thanks for the support!

[@ParkourCrewGFC]

Awesome video!! I'm a Physics student and this really helps me for my Linear Algebra final test :D

[@brightsideofmaths]

Thank you :)

[@PunmasterSTP]

How'd your final go?

[@ichleckererkeks]

Super erklärt, uns wurde extra empfohlen Videos zu dem Thema lieber anzuschauen. So versteht man Lineare Algebra direkt. Danke :)

[@brightsideofmaths]

Thanks :)

[@nerses2654]

really helped me to understand course of linear algebra.thanks

[@tithisarkar2987]

thanks a lot sir,you are amazing,lots of respect

[@thomasyoung398]

Thank you for the explanation. Very easy to understand.

[@brightsideofmaths]

Glad it was helpful!

[@nicolas.m5]

thanks so much for existing

[@brightsideofmaths]

Thanks for your support :)

[@anuragreghu827]

Really good content. Very informative and good articulation.

[@brightsideofmaths]

Thank you very much! I hope that you can also enjoy the other parts about the Jordan normal form :)

[@vijaysinghchauhan7079]

thank you for this amazing example and explanation.

[@isaaclafts7152]

Great video!

[@mikiasberhanu8509]

Jordan block is something new for me and I wanna know why do we put one next to the box ? What is the reason if you can please explain it. The videos are clean and easy to understand. Thank you

[@xyip3382]

Your videos are so great.

[@azenora8150]

Hello, I'm sorry this video is a little bit old, but I have a question: why if the geometric multiplicity is 2 we will have just one possibility which is a box of size two in first and a box of size one after and not conversely? I mean: a box of size one in first and of size two after? (Otherwise thank you for all your video, they are very helpfull)

[@brightsideofmaths]

Thank you very much! The video is still up-to-date, I hope :) Regarding your question: You shouldn't see reordering of the boxes as new possibilities. Essentially this would be the same thing. Therefore, some people just have the convention to start with the largest box to avoid confusion.

[@anouaracheghaf6220]

this is great !!

[@jordanshoo-l8l]

thank you

[@brightsideofmaths]

Thank you for your support :)

[@lurimay_jett]

So according to the fundamentl theormem, rank(M) + Nulity(M)=n, also, taking that in to account, i saw in class that rank(A-lambda Identity) - nulity(A-lambda Identity)=n of the matrix after you substract the lambda from the main diagonal, i know you got in the video that the Ker(A-lambda Identity)=2 because of the independently linear vectors, however i cannot seem to understand why the guassian elimination went that way and how, instead, you can demonstrate this with the rank.

[@ukashish001]

Can you tell me which software do you use? Thank you. Nice Video

[@brightsideofmaths]

Xournal :)

[@lasithaamarasinghe9251]

nice video. understood the method🤩

[@brightsideofmaths]

Nice! Thanks. Maybe the other videos in the series also help you :) thebrightsideofmathematics.com/courses/jordan_normal_form/overview/

[@anowarali668]

thanks. in the second possibility in time of choosing box of eigen value 4 you have choosed first upper block with two 4 . what if i choose the lower two 4 in a block?

[@usercommon1]

Спасибо брат...

[@debarghyasaha7938]

best tutor ♥️

[@ma.hzadeh2776]

Thanks for the great video! Could you please explain more about how you determined the det?

[@brightsideofmaths]

You mean calculating the determinant?

[@ma.hzadeh2776]

@@brightsideofmaths yes

[@brightsideofmaths]

I have some videos about the determinant here. However, there are in German, but explain the calculation rules :)

[@ma.hzadeh2776]

@@brightsideofmaths Thank you! but I don't know German!

[@brightsideofmaths]

@@ma.hzadeh2776 Don't worry. English versions come soon :)

[@ParkourCrewGFC]

Great video, keep it up :D

[@icandothisallday986]

Please help. Desperate student here. The conclusion is now we can say there is some matrix P such that A=P.J.P^{-1}, where J is the matrix we just computed. How to find such a P? What is the algorithm to find such a P?

[@OnlyOnePlaylist]

Hey ! At 6:45, I don't understand why you say that we only need to compute the Geometric multiplicity and not the generalized eigenspaces to obtain the Jordan Normal Form

[@OnlyOnePlaylist]

What makes it so that we don't need to do step 3) ?

[@brightsideofmaths]

@@OnlyOnePlaylist In this example, the dimensions of the generalized eigenspaces are already clear, see the three possibilities.

[@jirinovak2389]

good job india man

[@中文中国-t4u]

update please 🥺

[@albertluo5273]

what if the geometric multiplicity is 0

[@brightsideofmaths]

Geometric multiplicity of zero means that there is no eigenvector which means that λ was not an eigenvalue. In other words: This can't happen in this context.

[@PunmasterSTP]

Yeah this tripped me up as well, but what he said eventually dawned on me. If there isn't any vector that is sent to that scalar multiple of itself, then the "eigenvalue" isn't really an "eigenvalue"!

[@james_white]

Why are x2 and x4 the free variables? Is it because they have a 1 in the column? And if so what is stopping you from doing row 2 multiplied by 1/4 to make the 4 into 1?

[@brightsideofmaths]

Free variables correspond to the columns where there are no pivots.

[@emrekayacikx]

Which English accent is this? sound cool

[@brightsideofmaths]

Probably a German accent.

[@mohammedsamir438]

❤️👏👏👏❤️

[@cooking60210]

Wait, a video on Jordan form that's actually accurate??? That never happens!

[@brightsideofmaths]

Yes, and I have four of them :) See here: tbsom.de/s/jordan

[@中文中国-t4u]

update please 🥺

[@中文中国-t4u]

update please 🥺

[@brightsideofmaths]

What do you mean?