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.
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.
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.
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.
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)
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.
Don't forget to download the PDF version with the link in the description! :)
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.
Nice work :)
Is this true? What is happening 😳- I just slipped into a parallel universe I think!
You forgot to mention that he was born in Jordan.
Now the *World economic form is using it... it's everywhere.... I feel like Jim Carrey right now😆😆😆
Just like the Foucault pendulum was invented by Michel Foucault.
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.
I just started reviewing linear algebra, this is epic.
I came across this when studying for a course. Really helped me understand the Jordan normal form.
Thank you!!!!
How have your classes been going?
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.
Man this is GREAT! Really well explained and easy to understand, and amazing presentation! You got yourself a sub!
Thanks a lot :)
Clear Explanation about Jordan form.. thx
Articulate, Concise, Perfect!
Thank you from France 🇫🇷 !!
Thank you so much!! Keeping me alive in this subject.
I take it you are a student, and if so, how have your studies been going?
Omg, I literally have an exam tomorrow on this topic, that was unexpected.
P.S. Thank you for your measure theory videos, they are awesome.
How did your exam go and how have your classes been going?
it's an amazing presentation, great sir. I have learnt a lot from this video ❤❤
Glad to hear that! And thanks for your support!
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.
Maybe you didn't see the difference between Jordan blocks and Jordan boxes?
sir thank you for all you do! 😊
Good morning sir 🙏🙏🙏🙏🙏, very nice explanation sir, keep it continue
Thank you very much!
It's beautiful!
Thank you very much sir very nice video very good.
Love the video, it helps a lot thanks👌
Thank you for the support :)
hats off for the amazing lecture.
Thank you very much :)
Jordan normal form? More like "Jeez, I wish this level of education were the norm!" Thanks for making such interesting and accessible videos.
thank you so much
Thank you! It really helped me!
You are very welcome :)
Thanks legend !
Great video, thank you!
OMG! Thanks a lot!
Thank you!
Can you explain why there's 1 over the diagonal ?
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)
you really explained well thank you
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.
Thanks :)
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
You see this for the third power:
A^3 = X J X^{-1} X J X^{-1} X J X^{-1}
@@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?
Wow, this is great
Love from India😍
Thank you sir
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.
I guess, the next parts will really help you :)
Great explanation :)
Thanks a lot :)
what book are you using
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.
@@brightsideofmaths thank's for ask
It's helpful
Where do the ones come from?
What is geometric multiplicity you didn't explain
Dimension of the corresponding eigenspace. In part 2, I calculate an example :)
Thank you.
You're welcome 😊
I love you
cake-u-late (nice video!)
watching this the night before the exam: 🐵
How did your exam go?
What kind of accent is that?
I guess it's french
German, I guess :D
You are just telling how to write Jordan normal form , but how does it come ?
Therefore 4 parts and a whole linear algebra course on the channel :D
I must be the Jordan abnormal form
Lol!
thanks much! anyone in math110 at berkeley lol
I didn't go to Berkeley, but how have your studies been going?