Jordan Normal Form - Part 1

Jordan Normal Form - Part 1 - Overview

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Күн бұрын

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This is my video series about Linear Algebra. I hope that it will help everyone who wants to learn about it.
This video is about the Jordan normal form, which is a matrix decomposition for square matrices. I show the idea and the algorithm with the help of an example. In further videos, I explain the details.
00:00 Introduction
00:57 Definition "diagonalizable"
03:50 Example
05:35 Jordan blocks
07:00 Jordan boxes
11:49 Recipe
I hope that this helps students, pupils and others. Have fun!
#LinearAlgebra
(This explanation fits to lectures for students in their first and second year of study: Mathematics for physicists, Mathematics for the natural science, Mathematics for engineers and so on)

Пікірлер: 82

@brightsideofmaths 2 ай бұрын

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

@1tuface963 2 жыл бұрын

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 2 жыл бұрын

Nice work :)

@charlesdaugherty9155 Жыл бұрын

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

@nachiketa9245 Жыл бұрын

You forgot to mention that he was born in Jordan.

@charlesdaugherty9155 Жыл бұрын

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

@seneca983 Жыл бұрын

Just like the Foucault pendulum was invented by Michel Foucault.

@imatreebelieveme6094 Жыл бұрын

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.

@newkid9807 4 жыл бұрын

I just started reviewing linear algebra, this is epic.

@marlonabeln8234 3 жыл бұрын

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

@PunmasterSTP 2 жыл бұрын

How have your classes been going?

@HuyNguyen-fp7oz 3 жыл бұрын

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.

@ar3568row 11 ай бұрын

Articulate, Concise, Perfect!

@satheeshbrcm 3 жыл бұрын

Clear Explanation about Jordan form.. thx

@astyutechick7980 3 жыл бұрын

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

@brightsideofmaths 3 жыл бұрын

Thanks a lot :)

@matissesaint-ghislain1786 3 жыл бұрын

Thank you from France 🇫🇷 !!

@johnkay1952 Жыл бұрын

Great video, thank you!

@madaaz6333 4 жыл бұрын

It's beautiful!

@MrDor890 3 жыл бұрын

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

@PunmasterSTP 2 жыл бұрын

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

@putin_navsegda6487 2 жыл бұрын

sir thank you for all you do! 😊

@loo2355 3 жыл бұрын

Thank you!

@geethamonnappa4645 2 жыл бұрын

you really explained well thank you

@julioperezv.4614 2 жыл бұрын

thank you so much

@cantorbernoulli4407 5 күн бұрын

Thanks legend !

@MrLucario127 2 жыл бұрын

OMG! Thanks a lot!

@galqiwi 4 жыл бұрын

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

@galqiwi 4 жыл бұрын

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

@PunmasterSTP 2 жыл бұрын

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

@ma.hzadeh2776 Жыл бұрын

Thank you! It really helped me!

@brightsideofmaths Жыл бұрын

You are very welcome :)

@shaliniverma9057 2 жыл бұрын

Thank you sir

@areaofthepyramid8336 2 жыл бұрын

Wow, this is great

@eugenethegod 3 жыл бұрын

Thank you very much sir very nice video very good.

@jaredjones6570 2 жыл бұрын

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)

@lunt5348 Жыл бұрын

Love the video, it helps a lot thanks👌

@brightsideofmaths Жыл бұрын

Thank you for the support :)

@vijaysinghchauhan7079 Жыл бұрын

hats off for the amazing lecture.

@brightsideofmaths Жыл бұрын

Thank you very much :)

@janvinarula4908 3 жыл бұрын

It's helpful

@jasonbroadway8027 Жыл бұрын

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 Жыл бұрын

Thanks :)

@sofiane90 3 жыл бұрын

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

@matharya653 8 ай бұрын

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

@brightsideofmaths 8 ай бұрын

Glad to hear that! And thanks for your support!

@mauricioconlaparva Жыл бұрын

Great explanation :)

@brightsideofmaths Жыл бұрын

Thanks a lot :)

@calberk1737 3 жыл бұрын

Where do the ones come from?

@PunmasterSTP 2 жыл бұрын

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

@pramilakumari9130 3 жыл бұрын

Love from India😍

@zingywingy 2 жыл бұрын

Thank you.

@brightsideofmaths 2 жыл бұрын

You're welcome 😊

@warrevdb6987 Жыл бұрын

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 Жыл бұрын

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

@bhupendragupta3120 Жыл бұрын

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

@brightsideofmaths Жыл бұрын

Thank you very much!

@lordself 2 жыл бұрын

what book are you using

@brightsideofmaths 2 жыл бұрын

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 2 жыл бұрын

@@brightsideofmaths thank's for ask

@utkudenizaltiok860 3 жыл бұрын

What is geometric multiplicity you didn't explain

@brightsideofmaths 3 жыл бұрын

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

@user-dx9gi8ql2c 2 ай бұрын

I love you

@ThuongPham-wg4bc 2 жыл бұрын

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 2 жыл бұрын

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

@ThuongPham-wg4bc 2 жыл бұрын

@@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?

@gabrielhaeser4061 4 жыл бұрын

cake-u-late (nice video!)

@Albeit_Jordan 2 жыл бұрын

I must be the Jordan abnormal form

@PunmasterSTP 2 жыл бұрын

Lol!

@matyezda 3 жыл бұрын

watching this the night before the exam: 🐵

@PunmasterSTP 2 жыл бұрын

How did your exam go?

@AB-uf5js 2 ай бұрын

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 2 ай бұрын

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