The fact that you provide all these high quality science content for free of cost, simply proves that you are a truly passionate science communicator and educator.
I have to say I am unsure, since he usually produces stuff that centers around himself - but he would have found it to be particularly difficult to produce this video.
I was so depressed from college and the fact that I can not follow up with my classmates. BUT NOW, I feel I can explain to the whole class. Thanks a lot plz keep your work! You are amazing.
The most simplified explanation of eigen value & eigen vector. I was struggling a week to understand what eigenvalue really is. Thank you so much for such a beautiful simplied explanation.
12:20 We could also use following determinant property: If matrix "A" is either a upper triangular matrix, a lower triangular matrix or a diagonal matrix, then its determinant is equal to product of the items from its main diagonal. For example: Case 1) "A" is upper triangular matrix: | 1 2 3 | | 0 5 6 | | 0 0 9 | Then det(A) = 1 * 5 * 9 Case 2) "A" is lower triangular matrix: | 1 0 0 | | 4 5 0 | | 7 8 9 | Then det(A) = 1 * 5 * 9 Case 3) "A" is diagonal matrix: | 1 0 0 | | 0 5 0 | | 0 0 9 | Then det(A) = 1 * 5 * 9 Source: en.wikipedia.org/wiki/Determinant#Properties_of_the_determinant See rule number "7.".
1) 02:50 - 04:43 Whoa, you have explained this topic very easily and understandable :) I was always wondering why we calculate "λ" from exactly this condition: det(A - λ*I)=0. Now I know that, thanks a lot :) 2) 07:53 - 08:24 and 10:12, 11:14 - This is also a very useful knowledge. You not only learn HOW TO CALCULATE, but also EXPLAIN WHY it is calculated exactly that way.
@@braydenchan138 Ah, I was just referencing his intro :D I believe he later on changed the intro jingle to "He knows a lot about the science stuff, here's Professor Dave Explains!"
Dave, you are amazing. You are my real linear algebra teacher. I learned more from your 17 minute video than I did from 4 hours of class. I can't express how much I appreciate it!
At 12:19, you can simply skip using Sarrus' rule for the 3x3 matrix. Since it has all 0s on one side of the diagonal, you can simply directly multiply the elements along the diagonal to get the determinant. This applies regardless of whether the 0s are on the top right or bottom left. You could also perform row operations until the matrix becomes triangular, then multiply along the diagonal to get the determinant.
Came back one year later when I had to revisit this topic for one of my courses, and I find that your video is still the best on the subject! I had already liked the video last year 😄, I would've loved to re-like. Good job.
You're doing an AMAZING job Professor Dave! Your videos are so much easier to understand than the way my professor explains it. It's all clear now. Thanks for existing!
Thank you!! I went through 5+ videos on this topic including a paid course on Coursera and this is still the best, most straightforward, thorough and succinct explanation I've seen to date. You've got yourself a new sub.
Thanks for showing all the steps needed to find both Eigenvalues and Eigenvectors without skipping over the algebra involved, helpful for someone like me who is a long time out of school coming back to learn Linear Algebra a second time around.
Thank you so much, Professor Dave. I just discovered your channel after struggling with eigenvalues and eigenvectors. You made the entire learning process easy with your clear and easy-to-understand explanations. Thank you once more.
That is so concise and clean! Thank you so much! You just used 20 minutes to help me understand something I confused so much after listening to a lecture entirely about it.
I used these in school but never developed an intuitive understanding. Now I’m trying to understand some control theory a little better and these are really important. I was pleasantly surprised to find you made a video when I went searching for content. My combined college diff eq/lin algebra class probably cost me $2500 and now you have RU-vid professors providing better explanations and visualizations for free. Fourier and Laplace transforms sailed right over my head and now I feel like I could explain them to anyone with a high school level education.
this is the best youtube video to explain eigenvalues and eigenvectors, only thing is that when it explains 3x3 matrix, probably it will be even better if it provide the generic forms of the eigenvectors (it did give generic forms when explains 2x2 matrix. An excellent video!
The row echelon thing around 9 minutes is wasting time for no gain. If you don't do it, you get the same equation for x_1 and x_2, plus another one which is just a scalar multiple of the first and therefore has the same solution. Impressive that I've got this far into the series without a single criticism or suggestion! Amazing stuff, Prof D, thank you.
Oh my GOD. I could for the life of me not comprehend eigenvectors the way my prof taught us. He taught an overcomplicated way of finding eigenvalues so THAT was a lot to unpack. This is so much easier! This is the FIRST video explication i had to watch in the whole first year of uni... goes to show how overcomplicated it was. Tho for eigenvectors it could've been explained a little bit better because what we do is setting x1 to 1 and removing the first row for Lambda 1. Then setting x1 to 1 and removing 2nd row for Lambda 2 And so on. Tbh i have no idea if it's ok to do it like this but this subject has drained me so much to the point i don't even care anymore
Thanks for refreshing my memory from the course I had 30 years ago! You explained it very well and I enjoyed a lot. Thank you! I also have a question. When I use PCA on a dataset in R , where is matrix A? I may have for example 10 columns (fields) and millions of records which means that my dataset is not a squared matrix. I can't understand how Eigenvalues and Eigenvectors are calculated for a non squared matrix. Also can I call each column a new eigenvector? Thanks for your attention and hope to have an answer from you. Once again thanks for teaching mathematical concepts.
At the end of the video for the eigenvalue whose value is 2 I would like to ask if it's also possible that it's corresponding eigenvector would also be (5,-1) since 1x(1)+5x(2)=2 if you put in X1 a value of 5 and in X2 a value of -1 the result would still be zero isn't it?
Yes, that is called the trace of the matrix. The determinant is the product of the eigenvalues. The trace and determinant are two values that can be used as shortcuts to finding the eigenvalues more directly. Call the mean of the diagonal, m, which will be half the trace of the matrix. Call the determinant p, for the product of the eigenvalues. The solution for eigenvalues: m +/- sqrt(m^2 - p)
This is the first time I have watched a youtube video and actually found it to be astronomically better than my professor. I know this comment is cliche but for real, I am impressed
