The Jacobian Matrix

In this video we discuss the concept of the Jacobian matrix. If given a function with multiple inputs and multiple outputs, the Jacobian matrix is a matrix of partial derivatives that measures the sensitivity of each output with respect to each input. This is the multi-dimension extension of the concept of the gradient of a function.
Topics and timestamps:
0:00 - Introduction
0:45 - Derivative
5:53 - Gradient
12:42 - Jacobian
24:15 - Example 1
27:04 - Example 2 (nonlinear to linear ODE)
Lecture notes and code can be downloaded from github.com/clum/KZread/tree/...
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Пікірлер: 26

  • @ChristopherLum
    @ChristopherLum4 ай бұрын

    In case it is helpful, here are all my calculus videos in a single playlist kzread.info/head/PLxdnSsBqCrrGHwNWnP5XVhytcGL9ExuPE. All my control theory videos are at kzread.info/head/PLxdnSsBqCrrF9KOQRB9ByfB0EUMwnLO9o . You can support this channel via Patreon at www.patreon.com/christopherwlum or by clicking on the 'Thanks' button underneath the video. Please let me know what you think in the comments. Thanks for watching!

  • @edwardmau5877
    @edwardmau5877Ай бұрын

    AE 512: You made the Jacobian a lot simpler to understand, especially with the point that it's basically just multiple gradients stacked on top of each other. Thanks.

  • @davidtelgen8114
    @davidtelgen8114Ай бұрын

    AE 512: Showing how this all connects with higher order topics like neural networks was eye opening, thank you!

  • @theminertom11551
    @theminertom1155124 күн бұрын

    Professor Lum, I am not saying this for any other reason than you deserve praise for how well you teach. I am sure that you were born just about the time that I received my BSEE but if at that time, my teachers had been able to explain the material that you teach (aerodynamics, calculus, vector calculus, etc.) as well as you teach it, then I think that I would really have learned it!

  • @ChristopherLum

    @ChristopherLum

    24 күн бұрын

    Thanks for the kind words, I'm glad you find the videos engaging and interesting. Please let me know if you have any thoughts or feedback on any of these topics or if you have suggestions for future content. Thanks for watching!

  • @theminertom11551

    @theminertom11551

    22 күн бұрын

    @@ChristopherLum Hi Professor, I do have some suggestions as to future content and I am a patrion member. Having watched this video to the end, I caught where you said that you were going to approach machine learning from a control systems point of view (neural networks). I am looking forward to this. About two years ago, I took my first step in the direction of machine learning with a video that I made concerning Augmented Reality, and here is the link. kzread.info/dash/bejne/in-dkrZ_mdGsmMo.html . I used a fairly generic software algorithm at the time called YOLO (you only look once). I look forward to a deeper understanding of the back propogation path which I am sure that you will show in terms of neural networks, which is a level "deeper" than machine learning.Training the algorithm took about two days...could have been better but I had had enough. At present, I am learning Python for DSP applications, which one could just call mathematical python. Most of machine learning, other than those that program their GPU's in CUDA are done in Python. BTW, my first programming language that I learned as an EE was Fortran, which I programmed with "punch cards", which, was kind of a nightmare. I also did a video, when I was getting my A&P on explaining why a propeller needs a twist, which you can see here. kzread.info/dash/bejne/oZyX2a-Me8K_ltY.html. That was done in Solidworks. Looking forward to these lectures.

  • @ChristopherLum

    @ChristopherLum

    22 күн бұрын

    @@theminertom11551 Tom, thanks for the detailed discussion. I watched your video on the smart glasses, that is pretty cool! I'm actually surprised that you had to program this yourself. Did the glasses not come with an API that enables this functionality natively? Thanks for following up on Patreon as I just discovered that because we're having this discussion on a thread of a comment in which I already responded to earlier, KZread doesn't notify me when subsequent posts/discussions are made.

  • @chnaka7518
    @chnaka75182 ай бұрын

    What a video abput Jacobian matrix. I have been searching a simple explanation for this topic. But I found more than what I have been searching for. Everyone can understand what you are teaching without getting into a stuck. Thank you Christoper Lum

  • @aimeepak717
    @aimeepak717Ай бұрын

    AE512: Watching this video as a refresher was the right choice :)

  • @ChristopherLum

    @ChristopherLum

    Ай бұрын

    I'm glad it was helpful! Keep me posted on how the linearization code goes.

  • @kenankenan6371
    @kenankenan6371Ай бұрын

    Please dear professor never stop doing this invaluable video-lectures. Also can't wait for your Kalman filters & Pontryagin's max principle lectures

  • @edriyin
    @edriyin4 ай бұрын

    This is a very well timed video for my graduation project which is designing 6DoF robotic manipulator. Thank you Dr. Lum. 🥳

  • @mateobalcorta9480
    @mateobalcorta94803 ай бұрын

    Love coming upon amazing lectures like Christopher Lum. Clearly explaining concepts with images included and also in an engaging manner. Keep up the good work. Look forward to watching more videos!

  • @jorymil
    @jorymil4 ай бұрын

    Great review of this stuff for me. I haven't dealt with Jacobians in a very long time....

  • @mohammedamr2
    @mohammedamr24 ай бұрын

    Thank you so much for these videos, i really enjoy every single video you have on your channel its very useful and informative, thank you sir.

  • @gman8217
    @gman82174 ай бұрын

    i havent watched the video yet but i know itll be another banger thanks bro

  • @okarakoo
    @okarakoo2 ай бұрын

    Extremely well done, thank you! 🙂

  • @wiloberlies9598
    @wiloberlies95984 ай бұрын

    Awesome stuff once again Dr Lum, thank you so much.

  • @ChristopherLum

    @ChristopherLum

    4 ай бұрын

    Great to hear from you Wil, glad you enjoyed it!

  • @PerceptorM
    @PerceptorM3 ай бұрын

    Thanks for the video. Great explanation of a Jacobian Matrix. :)

  • @WalkingDeaDJ
    @WalkingDeaDJАй бұрын

    Jason-AE512: Even though this is a optional video, but I still learn a lot.

  • @zakzqk8485
    @zakzqk84854 ай бұрын

    Thank you so much Dr

  • @aron2971
    @aron2971Ай бұрын

    Aasome videoooo.

  • @StarfallWarrior
    @StarfallWarrior4 ай бұрын

    Bagi skrip manimnya bang

  • @md.hamidulhaque5816
    @md.hamidulhaque5816Ай бұрын

    Just wastage of time. Where is the intuition behind Jacobian matrix ? Just a rubbish content !!!