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.".
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!
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!"
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.
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.
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!
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.
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.
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 RUclips 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.
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 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!
Sir, do I have to only choose X1 as 1? Or I can also choose X2 as 1 and then find corresponding value of X1? Because my answer is exactly reverse of what is being shown on screen at 16:35
It is arbitrary how large you define the eigenvectors to be, or which term to which you assign a value. But to keep it simple, you usually default to assigning one of the components of them to be unity, and you usually default to assigning it to the first element (x1). You can assign x1 to be 314 if you like, and the other terms of the eigenvector will follow proportionally. It is common that in applications of eigenvectors, it doesn't matter how large you make the eigenvectors, as their magnitude ends up cancelling out of the equation.
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
AAAHHH! Quantum class flashbacks!!!! Seriously, I noticed the lack of viewers on this. It's just a case of people being afraid of math. Kudos to everyone who watched the whole thing. 7:20 This is why mathematicians hate physicists. "OK, let's set the speed of light to 1 with no units. We'll put it back in when we need it." 15:40 You can think of the "free variable" as integration in calculus. When you take the derivative of an equation, you lose the finale constant. When you turn around and integrate the equation, you an add a constant of any value. IRL, acceleration is the derivative of velocity. Going the other way, velocity is the integral of acceleration. So what's the +c? It's your starting velocity. For example, you are in your car and accelerate 1 kph/sec. So how fast are you going after 10 seconds? One bit of information is missing, that is, your initial velocity. It's the difference between hitting the gas when the light turns green, verses hitting the gas to pass a slow poke. However, this matrix math can only be solved for integral values, which pretty much is basis of quantum mechanics, As I've told people before, you really can't understand the whys and hows of QM without doing the math.
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?
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.
How do I know what value to choose for the x when finding the eigenvectors. When I tried doing it, I got [1 ,-1/5] and I want to know how you would get the right value. Thanks!
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.
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😭
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.".
cool
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_
five hours... pulling an all nighter for this
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!
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 RUclips. 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
I am watching this video at 1AM the day prior to a biostatistics exam. You are a gift from God.
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
Thanks!
The way you explained everything step by step and clear way shows your invaluable knowledge in science thank you for providing this for free!
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.
You are an actual lifesaver, managed to catch up on the subject in just three days with your playlist.
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.
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!
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.
I am taking this lecture one day before my exam and this is really helpful...what a way of teaching ...superb
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.
Thank you so much for these videos. You really explain them so simply and it is so easy to understand.
This has got to be the simplest explanation of eigen vectors and values. Thank you
I still love that intro.
I cannot express how much I want to thank you man
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.
My teacher for Linear algebra has a very confusing way of teaching, thank you so much for making it do simple
They should put your name on my diploma because you are single-handedly getting me through college
Great video, liked the simple explanation of why the det(A) is to be zero to get a non-trivial solution of Ax=0
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!)
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 RUclips 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.
I love your videos so much professor Dave. You just make everything so simple and very easy to understand. Thank you so much professor Dave ❤
great explanation appreciated a lot !!!! I understood now I couldn"t get it from the lectures.
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
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!
Incredible how you explain these things so clearly and so accurately even though you're not a math major (that's a compliment). Kudos!
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!
Unbelieveable! The most clear tutorial I've ever seen. Thanks!
hi can you explain on the point where you choose x1=1 to obtain the eigenvector for /l=2
time 10:00
This explanation helps in providing a clearer picture of the topic Thank you so much Sir 🙏🏻
Thank you, this was a clear explanation
Man rly explained my 2hr lecture which I couldn't comprehend in 20 mins of which I now understand
Professor Dave, you taught well in this video. I understand how to solve for eigenvalues and eigenvectors. Thank you for posting this video.
Your videos are too good and too helpful.. Thanks a lot Professor ❤️
you are the true definition of Professor Thumbs up
You're the best, man! You make things seem so easy. Wish I meet you someday ❤
You have no idea how much you helped me. Thanks!❤
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.
16:46 I completely understand this topic now, thanks a lot
This guy is the boss, I learnt very quickly
Only person alive who can explain maths clearly
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!
Thanks professor for making linear algebra simple
this man is always a lifesaver
thanks professor. grateful from IIT, thanks for helping at the last moment of midsem exams. i have midsem exam in 3 hr.
Sir, do I have to only choose X1 as 1? Or I can also choose X2 as 1 and then find corresponding value of X1?
Because my answer is exactly reverse of what is being shown on screen at 16:35
so is it the right answer as well? or is it wrong?
It is arbitrary how large you define the eigenvectors to be, or which term to which you assign a value. But to keep it simple, you usually default to assigning one of the components of them to be unity, and you usually default to assigning it to the first element (x1). You can assign x1 to be 314 if you like, and the other terms of the eigenvector will follow proportionally.
It is common that in applications of eigenvectors, it doesn't matter how large you make the eigenvectors, as their magnitude ends up cancelling out of the equation.
I had same issue. Same magnitude of eigen vectors but reversed signs. Is it acceptable?
Just watched a 2 hour lecture. 6 min into this video I've learnt more , amazing and thank you sir
super simple
you are the best sir, i salute you dear🙋🙋🙋🙋🙋🙋🙋🙋
Just took me minutes to realize how to find out eigenvectors. Thanks a lot
Thank you so much . You are the awesome teacher in the world. I wish you are also my school teacher
This is like insane teaching! you have made it sooo easy to understand this, thankyou Professor Dave!
Very crystal clear explanation. Thank you.
I wish you a great day, sir, im sure you've got many more video explanations like this on your channel.
16:01: the eigenvector for lambda = 4, shouldnt it be where c can be any real number, instead of ?
Thanks for helping me open my mind, you're better than my lecture at my university that i could easily get it
thank you for what you do. I need to see multiple perspectives (explanations) on a topic to fully get it!
This is genius.. i have no words!Thank you so much!!!
I'm trying to master eigens to code my algebraician level skill nodes in my Mentat project. Thanks, Dave!
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
Great day to need to describe natural frequencies of vibrations and separate modes of motion 🙏
I am glad to reach this illustration !!! Super Clear
GREAT EXPLANATION, thanks alot
Beautiful explanation, Thank you very much 🙏
9:30 what is the purpose of putting the matrix in row echelon form? I feel like that is left unexplained.
You explained it clearly than my professor. Thank you!
AAAHHH! Quantum class flashbacks!!!!
Seriously, I noticed the lack of viewers on this. It's just a case of people being afraid of math. Kudos to everyone who watched the whole thing.
7:20 This is why mathematicians hate physicists. "OK, let's set the speed of light to 1 with no units. We'll put it back in when we need it."
15:40 You can think of the "free variable" as integration in calculus. When you take the derivative of an equation, you lose the finale constant. When you turn around and integrate the equation, you an add a constant of any value. IRL, acceleration is the derivative of velocity. Going the other way, velocity is the integral of acceleration. So what's the +c? It's your starting velocity. For example, you are in your car and accelerate 1 kph/sec. So how fast are you going after 10 seconds? One bit of information is missing, that is, your initial velocity. It's the difference between hitting the gas when the light turns green, verses hitting the gas to pass a slow poke.
However, this matrix math can only be solved for integral values, which pretty much is basis of quantum mechanics, As I've told people before, you really can't understand the whys and hows of QM without doing the math.
you are a saint. there is no way to thank you enough.
He knows a lot about this kind of stuff!
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?
No words, thank you so much sir.
Detailed and easy to understand，thank you
I need to go back and learn some more before this, but I still watched the entire video. Keep up the great work, man!
If you keep watching, you'll see Quantum Mechanics elegantly derived from this math.
Thank you for this tutorial. Very easy to follow.
Thats the craziest intro ever, love love love lol
I literally have exam in 23 seconds, thank you Professor
Thank you so much professor, u literally saved my day!
Great explanation.
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.
A subbed to you without thinking i really understood everything
@Professor Dave Explains may God bless you.
How do I know what value to choose for the x when finding the eigenvectors. When I tried doing it, I got [1 ,-1/5] and I want to know how you would get the right value. Thanks!
Also fell on same trap, decided to multiply by 5 but got answer with reversed signs. Even the second eigen vector had reversed signs. I wonder why.
They are technically the same form. he just chose x2 to be the 1, so x1 is relative to that. Its the same relationship between the values
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
Professor Dave you rock 😊
Just a side note: In the example (16:10) the matrix A has a -5 instead of 5.
Explained like charm