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.
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.".
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.
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.
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
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!"
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!! 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.
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.
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.
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!
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 TH-cam 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!
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.
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
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.
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)
![[#2024MAMA] ROSÉ (로제), Bruno Mars - APT. | Mnet 241122 방송](http://i.ytimg.com/vi/dgGqD28J6aQ/mqdefault.jpg)
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.
@@Yatukih_001 ...what?
@@Yatukih_001 ???
@@Yatukih_001 ????
@@Yatukih_001 shut your fxxk up
I self learned linear algebra with the help of your videos, the appreciation is not describable. Thank you so much professor Dave
He breaks every topic in such a beautiful way and most importantly easy to understand.
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.".
cool
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.
I literally have an exam in 4 hours, and you have no idea how grateful I am. Thank you Professor
@davidgarciagomez1387 Hope you'll pass it
@@user_30093just got out, probably passed so all great 😎☝️
4 hours and 6 minutes for me right now lmao
4hrs and 30mins for me here @@Schnapperlol_
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.
yeah for upper and lower triangular matrix, the determinant is simply the product of the main diagonal
And here comes the engineering students 1hr before their exam😂😂
15 min before😂
So real😂😂
The struggle is real!
An hour and half before lol
😂😂me right now😭
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.
(you make exactly this point in the next video!)
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
This channel is literally the essence of my college existence
funny how a guy on youtube explains it a lot better than a prof.
He's not just 'a guy' in TH-cam. He knows a lot of stuff just like a professor or a scientist
He is professor dave 😅
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.
Prof. Dave is really great!
@@braydenchan138 He certainly does know a lot about the science stuff
@@mikaelious9550 Could you explain more?
@@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!"
I GIVE UP WATCHING MY TEACHERS' LECTURE VIDEOS! YOU MAKE EVERYTHING SEEM SO SIMPLE. THANK YOU
The way you explained everything step by step and clear way shows your invaluable knowledge in science thank you for providing this for free!
You are an actual lifesaver, managed to catch up on the subject in just three days with your playlist.
I am taking this lecture one day before my exam and this is really helpful...what a way of teaching ...superb
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.
I am watching this video at 1AM the day prior to a biostatistics exam. You are a gift from God.
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.
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.
My teacher for Linear algebra has a very confusing way of teaching, thank you so much for making it do simple
Great video, liked the simple explanation of why the det(A) is to be zero to get a non-trivial solution of Ax=0
This has got to be the simplest explanation of eigen vectors and values. Thank you
It is nice to see this concept explained in a different light to how it was taught to me years ago. Nice video!
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.
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!
They should put your name on my diploma because you are single-handedly getting me through college
Thank you so much for these videos. You really explain them so simply and it is so easy to understand.
I still love that intro.
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 TH-cam 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.
You explained this process better than my professor...Thanks so much for your help! I understand how to calculate eigenvectors now!
Sad isnt it? You pay high tuition fee just for incompetent professors.
I cannot express how much I want to thank you man
great explanation appreciated a lot !!!! I understood now I couldn"t get it from the lectures.
Always didn't understand this stuff but after watching your video it makes way more sense. Thanks
Hell yeah gotta cram for my linear final tomorrow. Thanks for the refresh mate!
thanks professor. grateful from IIT, thanks for helping at the last moment of midsem exams. i have midsem exam in 3 hr.
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!
godamn pulling an all nighter loaded on coffee been procrastinating too long got an end of semester exam in 3 hours FEELING GOOD BABYYY!!!
Feel you bro, prolly going to end up doing the same, hope ya did well!
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.
Thanks professor for making linear algebra simple
you are the true definition of Professor Thumbs up
Man rly explained my 2hr lecture which I couldn't comprehend in 20 mins of which I now understand
16:46 I completely understand this topic now, thanks a lot
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
This explanation helps in providing a clearer picture of the topic Thank you so much Sir 🙏🏻
Great day to need to describe natural frequencies of vibrations and separate modes of motion 🙏
Thank you, this was a clear explanation
Just watched a 2 hour lecture. 6 min into this video I've learnt more , amazing and thank you sir
This guy is the boss, I learnt very quickly
Professor Dave, you taught well in this video. I understand how to solve for eigenvalues and eigenvectors. Thank you for posting this video.
Unbelieveable! The most clear tutorial I've ever seen. Thanks!
I'm trying to master eigens to code my algebraician level skill nodes in my Mentat project. Thanks, Dave!
Thank you so much . You are the awesome teacher in the world. I wish you are also my school teacher
You're the best, man! You make things seem so easy. Wish I meet you someday ❤
this man is always a lifesaver
Just took me minutes to realize how to find out eigenvectors. Thanks a lot
thank you for what you do. I need to see multiple perspectives (explanations) on a topic to fully get it!
Only person alive who can explain maths clearly
I literally have exam in 23 seconds, thank you Professor
Thanks for helping me open my mind, you're better than my lecture at my university that i could easily get it
I wish you a great day, sir, im sure you've got many more video explanations like this on your channel.
You have no idea how much you helped me. Thanks!❤
Incredible how you explain these things so clearly and so accurately even though you're not a math major (that's a compliment). Kudos!
9:30 what is the purpose of putting the matrix in row echelon form? I feel like that is left unexplained.
Very crystal clear explanation. Thank you.
You explained it clearly than my professor. Thank you!
Your videos are too good and too helpful.. Thanks a lot Professor ❤️
You are handsome and genius professor.
Thanks for helping me got through tests and examination
Geometrically, an eigenvector of a matrix A is a non-zero vector x in R to the power n such that the vectors x and Ax are parallel
This is genius.. i have no words!Thank you so much!!!
Today I learned that "eigenwaarde" and "eigenvector" translate very simple from Dutch into English.
Eigen is based on a German word for "self", that Euler coined, so it is understandable how this happened.
He knows a lot about this kind of stuff!
you are a saint. there is no way to thank you enough.
@Professor Dave Explains may God bless you.
Just a side note: In the example (16:10) the matrix A has a -5 instead of 5.
This is like insane teaching! you have made it sooo easy to understand this, thankyou Professor Dave!
Thanks, you save my linear algebra final 😭😭😭
I am glad to reach this illustration !!! Super Clear
GREAT EXPLANATION, thanks alot
hi can you explain on the point where you choose x1=1 to obtain the eigenvector for /l=2
time 10:00
Beautiful explanation, Thank you very much 🙏
Thank you for this tutorial. Very easy to follow.
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.
No words, thank you so much sir.
Did anyone notice that *sum of all diagonal entries = sum of all eigenvalues*
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)
Detailed and easy to understand，thank you
Thank you so much professor, u literally saved my day!
Explained like charm
you are unbelievable
Thank you so much for this simple explanation
Great explanation.
Thanks!
Excellent explanation. Thanks for this
10:02 for the vectors
The video has really helped me
A subbed to you without thinking i really understood everything
Thank you so much professor dave
amazing video. all issues solved.
Perfect, just perfect!