Jordan Normal Form 2 | An Example

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  • Опубліковано 21 січ 2025

КОМЕНТАРІ • 72

  • @zachchairez4568
    @zachchairez4568 4 роки тому +41

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

    • @PunmasterSTP
      @PunmasterSTP 3 роки тому +1

      How has your academic career been going?

    • @willadem8643
      @willadem8643 9 місяців тому +1

      This has to be the stupidest comment in the history of UA-cam. "Greatest Mathematicians on UA-cam" - 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
      @zachchairez4568 9 місяців тому

      @@willadem8643Are you ok?

    • @zachchairez4568
      @zachchairez4568 9 місяців тому +1

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

    • @PunmasterSTP
      @PunmasterSTP 9 місяців тому

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

  • @KogularajK.
    @KogularajK. 6 місяців тому +5

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

  • @alainmifsud3968
    @alainmifsud3968 3 роки тому +5

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

  • @lume.3887
    @lume.3887 Рік тому +4

    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.

  • @lucyferyx
    @lucyferyx 2 роки тому +6

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

  • @VaibhavKumar-zh5yu
    @VaibhavKumar-zh5yu 4 місяці тому

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

    • @brightsideofmaths
      @brightsideofmaths  4 місяці тому

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

  • @ParkourCrewGFC
    @ParkourCrewGFC 4 роки тому +9

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

  • @ichleckererkeks
    @ichleckererkeks 2 роки тому

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

  • @thomasyoung398
    @thomasyoung398 2 роки тому

    Thank you for the explanation. Very easy to understand.

  • @isaaclafts7152
    @isaaclafts7152 4 роки тому +4

    Great video!

  • @tithisarkar2987
    @tithisarkar2987 3 роки тому +2

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

  • @xyip3382
    @xyip3382 4 роки тому +1

    Your videos are so great.

  • @nerses2654
    @nerses2654 Рік тому

    really helped me to understand course of linear algebra.thanks

  • @anuragreghu827
    @anuragreghu827 4 роки тому +3

    Really good content. Very informative and good articulation.

    • @brightsideofmaths
      @brightsideofmaths  4 роки тому +1

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

  • @vijaysinghchauhan7079
    @vijaysinghchauhan7079 Рік тому

    thank you for this amazing example and explanation.

  • @anouaracheghaf6220
    @anouaracheghaf6220 4 роки тому +2

    this is great !!

  • @anowarali668
    @anowarali668 2 роки тому +1

    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?

  • @mikiasberhanu8509
    @mikiasberhanu8509 3 роки тому +1

    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

  • @ma.hzadeh2776
    @ma.hzadeh2776 2 роки тому

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

    • @brightsideofmaths
      @brightsideofmaths  2 роки тому

      You mean calculating the determinant?

    • @ma.hzadeh2776
      @ma.hzadeh2776 2 роки тому

      @@brightsideofmaths yes

    • @brightsideofmaths
      @brightsideofmaths  2 роки тому

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

    • @ma.hzadeh2776
      @ma.hzadeh2776 2 роки тому

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

    • @brightsideofmaths
      @brightsideofmaths  2 роки тому +1

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

  • @jordanshoo-l8l
    @jordanshoo-l8l 8 місяців тому

    thank you

  • @azenora8150
    @azenora8150 3 роки тому +5

    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
      @brightsideofmaths  3 роки тому +7

      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.

  • @OnlyOnePlaylist
    @OnlyOnePlaylist 7 місяців тому

    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
      @OnlyOnePlaylist 7 місяців тому

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

    • @brightsideofmaths
      @brightsideofmaths  7 місяців тому

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

  • @icandothisallday986
    @icandothisallday986 3 роки тому

    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?

  • @中文中国-t4u
    @中文中国-t4u Рік тому

    update please 🥺

  • @usercommon1
    @usercommon1 Рік тому

    Спасибо брат...

  • @ParkourCrewGFC
    @ParkourCrewGFC 4 роки тому +1

    Great video, keep it up :D

  • @debarghyasaha7938
    @debarghyasaha7938 2 роки тому

    best tutor ♥️

  • @lasithaamarasinghe9251
    @lasithaamarasinghe9251 7 місяців тому

    nice video. understood the method🤩

    • @brightsideofmaths
      @brightsideofmaths  7 місяців тому

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

  • @ukashish001
    @ukashish001 4 роки тому +3

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

  • @lurimay_jett
    @lurimay_jett 3 роки тому

    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.

  • @james_white
    @james_white 3 роки тому

    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
      @brightsideofmaths  3 роки тому

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

  • @albertluo5273
    @albertluo5273 4 роки тому +2

    what if the geometric multiplicity is 0

    • @brightsideofmaths
      @brightsideofmaths  4 роки тому +8

      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
      @PunmasterSTP 3 роки тому

      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"!

  • @emrekayacikx
    @emrekayacikx 3 роки тому +1

    Which English accent is this? sound cool

  • @jirinovak2389
    @jirinovak2389 3 роки тому +2

    good job india man

  • @mohammedsamir438
    @mohammedsamir438 2 роки тому

    ❤️👏👏👏❤️

  • @cooking60210
    @cooking60210 9 місяців тому

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

    • @brightsideofmaths
      @brightsideofmaths  9 місяців тому

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

  • @tariqemre
    @tariqemre 2 місяці тому

    First time no indian accent

  • @中文中国-t4u
    @中文中国-t4u Рік тому

    update please 🥺

  • @中文中国-t4u
    @中文中国-t4u Рік тому

    update please 🥺