The Jacobian Matrix
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- Опубліковано 26 чер 2024
- 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/UA-cam/tree/...
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You can support this channel via Patreon at / christopherwlum or by clicking on the ‘Thanks’ button underneath the video. Thank you for your help!
In case it is helpful, here are all my calculus videos in a single playlist ua-cam.com/play/PLxdnSsBqCrrGHwNWnP5XVhytcGL9ExuPE.html. All my control theory videos are at ua-cam.com/play/PLxdnSsBqCrrF9KOQRB9ByfB0EUMwnLO9o.html . 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!
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.
AE 512: Showing how this all connects with higher order topics like neural networks was eye opening, thank you!
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
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!
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!
@@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. ua-cam.com/video/XKi0TFinFhg/v-deo.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. ua-cam.com/video/ohcwMSK_Yfs/v-deo.html. That was done in Solidworks. Looking forward to these lectures.
@@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, UA-cam doesn't notify me when subsequent posts/discussions are made.
AE512: Watching this video as a refresher was the right choice :)
I'm glad it was helpful! Keep me posted on how the linearization code goes.
Please dear professor never stop doing this invaluable video-lectures. Also can't wait for your Kalman filters & Pontryagin's max principle lectures
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!
This is a very well timed video for my graduation project which is designing 6DoF robotic manipulator. Thank you Dr. Lum. 🥳
Extremely well done, thank you! 🙂
i havent watched the video yet but i know itll be another banger thanks bro
Great review of this stuff for me. I haven't dealt with Jacobians in a very long time....
Awesome stuff once again Dr Lum, thank you so much.
Great to hear from you Wil, glad you enjoyed it!
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.
Thanks for the video. Great explanation of a Jacobian Matrix. :)
Jason-AE512: Even though this is a optional video, but I still learn a lot.
Thank you so much Dr
Aasome videoooo.
Bagi skrip manimnya bang
Just wastage of time. Where is the intuition behind Jacobian matrix ? Just a rubbish content !!!