Jordan Normal Form 1 | Overview

[@brightsideofmaths]

Don't forget to download the PDF version with the link in the description! :)

[@1tuface963]

the jordan normal form was discovered by the famous mathematician micheal jordan in 1987. jordan was also known for his basketball career. Because this topic is one that mathematic students like the most, the company nike established the jordan shoe in honor of this beautiful topic.

[@brightsideofmaths]

Nice work :)

[@charlesdaugherty9155]

Is this true? What is happening 😳- I just slipped into a parallel universe I think!

[@nachiketa9245]

You forgot to mention that he was born in Jordan.

[@charlesdaugherty9155]

Now the *World economic form is using it... it's everywhere.... I feel like Jim Carrey right now😆😆😆

[@seneca983]

Just like the Foucault pendulum was invented by Michel Foucault.

[@imatreebelieveme6094]

Thanks for this. While German introductory maths courses often are very thorough on the theory, they often leave the specific algorithms to "figure it out on your own from the proof". This helps a lot.

[@marlonabeln8234]

I came across this when studying for a course. Really helped me understand the Jordan normal form. Thank you!!!!

[@PunmasterSTP]

How have your classes been going?

[@newkid9807]

I just started reviewing linear algebra, this is epic.

[@ar3568row]

Articulate, Concise, Perfect!

[@astyutechick7980]

Man this is GREAT! Really well explained and easy to understand, and amazing presentation! You got yourself a sub!

[@brightsideofmaths]

Thanks a lot :)

[@HuyNguyen-fp7oz]

I love your video a lot!!! Formal lectures often lack of motivation behind math concepts. I hope you would make more video explain advanced math subjects like this!!!! Your work will inspire many many students around the world to fall in love with math.

[@satheeshbrcm]

Clear Explanation about Jordan form.. thx

[@matissesaint-ghislain1786]

Thank you from France 🇫🇷 !!

[@MrDor890]

Thank you so much!! Keeping me alive in this subject.

[@PunmasterSTP]

I take it you are a student, and if so, how have your studies been going?

[@AB-uf5js]

5:47 Size of Jordan block corresponding to some eigenvalue isn't equal to its algebraic multiplicity. For one eigenvalue there can be (but don't have to be) more corresponding Jordan blocks and sum of their sizes is equal to algebraic multiplicity of a given eigenvalue.

[@brightsideofmaths]

Maybe you didn't see the difference between Jordan blocks and Jordan boxes?

[@galqiwi]

Omg, I literally have an exam tomorrow on this topic, that was unexpected.

[@galqiwi]

P.S. Thank you for your measure theory videos, they are awesome.

[@PunmasterSTP]

How did your exam go and how have your classes been going?

[@madaaz6333]

It's beautiful!

[@julioperezv.4614]

thank you so much

[@MrLucario127]

OMG! Thanks a lot!

[@loo2355]

Thank you!

[@eugenethegod]

Thank you very much sir very nice video very good.

[@cantorbernoulli4407]

Thanks legend !

[@putin_navsegda6487]

sir thank you for all you do! 😊

[@jaredjones6570]

What do you do with step 3 once the dim of ker matches the algebraic multiplicity after some power of (A-lambda*I) ? How do I use that to determine which jordan normal form is correct? (Edit: I will watch the next videos in the series so if it's answered there, thanks in advance)

[@sofiane90]

Can you explain why there's 1 over the diagonal ?

[@matharya653]

it's an amazing presentation, great sir. I have learnt a lot from this video ❤❤

[@brightsideofmaths]

Glad to hear that! And thanks for your support!

[@vijaysinghchauhan7079]

hats off for the amazing lecture.

[@brightsideofmaths]

Thank you very much :)

[@johnkay1952]

Great video, thank you!

[@ma.hzadeh2776]

Thank you! It really helped me!

[@brightsideofmaths]

You are very welcome :)

[@jasonbroadway8027]

Update: I now understand the video. I do not entirely understand the reason for the placement of the 1's, but I can follow the algorithm.

[@brightsideofmaths]

Thanks :)

[@areaofthepyramid8336]

Wow, this is great

[@PunmasterSTP]

Jordan normal form? More like "Jeez, I wish this level of education were the norm!" Thanks for making such interesting and accessible videos.

[@pramilakumari9130]

Love from India😍

[@geethamonnappa4645]

you really explained well thank you

[@bhupendragupta3120]

Good morning sir 🙏🙏🙏🙏🙏, very nice explanation sir, keep it continue

[@brightsideofmaths]

Thank you very much!

[@lunt5348]

Love the video, it helps a lot thanks👌

[@brightsideofmaths]

Thank you for the support :)

[@shaliniverma9057]

Thank you sir

[@mauricioconlaparva]

Great explanation :)

[@brightsideofmaths]

Thanks a lot :)

[@ThuongPham-wg4bc]

I wonder why when calculating the power of A, we just calculate the power of D. How about the power of X and X^-1? 1:45

[@brightsideofmaths]

You see this for the third power: A^3 = X J X^{-1} X J X^{-1} X J X^{-1}

[@ThuongPham-wg4bc]

@@brightsideofmaths Thank you sir. X^{-1}.X could be simplified to Identity matrix, so in the end we have X.J^3.X^{-1}, right?

[@warrevdb6987]

So for the example with the 2 jorden boxes in the jordan blok with the 3's how do you know which one is the correct jordan form and on what does it depend? could someone explain pls.

[@brightsideofmaths]

I guess, the next parts will really help you :)

[@zingywingy]

Thank you.

[@brightsideofmaths]

You're welcome 😊

[@janvinarula4908]

It's helpful

[@utkudenizaltiok860]

What is geometric multiplicity you didn't explain

[@brightsideofmaths]

Dimension of the corresponding eigenspace. In part 2, I calculate an example :)

[@lordself]

what book are you using

[@brightsideofmaths]

I don't use a book. I have written my own lecture notes (where I reference some books). You can find it on my website.

[@lordself]

@@brightsideofmaths thank's for ask

[@calberk1737]

Where do the ones come from?

[@gabrielhaeser4061]

cake-u-late (nice video!)

[@ArpanDasgupta-q4n]

I love you

[@matyezda]

watching this the night before the exam: 🐵

[@PunmasterSTP]

How did your exam go?

[@Jkfgjfgjfkjg]

What kind of accent is that?

[@alicezhou6252]

I guess it's french

[@brightsideofmaths]

German, I guess :D

[@Albeit_Jordan]

I must be the Jordan abnormal form

[@PunmasterSTP]

Lol!

[@suriyars4487]

You are just telling how to write Jordan normal form , but how does it come ?

[@brightsideofmaths]

Therefore 4 parts and a whole linear algebra course on the channel :D

[@GKinWor]

thanks much! anyone in math110 at berkeley lol

[@PunmasterSTP]

I didn't go to Berkeley, but how have your studies been going?