Finding Eigenvalues and Eigenvectors
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- Опубликовано: 7 июл 2024
- In studying linear algebra, we will inevitably stumble upon the concept of eigenvalues and eigenvectors. These sound very exotic, but they are very important not just in math, but also physics. Let's learn what they are, and how to find them!
Script by Howard Whittle
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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.
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.
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
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.
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!
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.
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.
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!"
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 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.
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 for these videos. You really explain them so simply and it is so easy to understand.
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.
The way you explained everything step by step and clear way shows your invaluable knowledge in science thank you for providing this for free!
Incredible how you explain these things so clearly and so accurately even though you're not a math major (that's a compliment). Kudos!
You are an actual lifesaver, managed to catch up on the subject in just three days with your playlist.
I GIVE UP WATCHING MY TEACHERS' LECTURE VIDEOS! YOU MAKE EVERYTHING SEEM SO SIMPLE. THANK YOU
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!
love this explanation! now that i have found your channel, i just move over to your math playlist every time i don't understand my university syllabus. thank you and keep up the great work! :))
Great video, liked the simple explanation of why the det(A) is to be zero to get a non-trivial solution of Ax=0
I still love that intro.
I am taking this lecture one day before my exam and this is really helpful...what a way of teaching ...superb
Professor Dave, you taught well in this video. I understand how to solve for eigenvalues and eigenvectors. Thank you for posting this video.
This has got to be the simplest explanation of eigen vectors and values. Thank you
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!
Your videos are too good and too helpful.. Thanks a lot Professor ❤️
thank you for what you do. I need to see multiple perspectives (explanations) on a topic to fully get it!
This is like insane teaching! you have made it sooo easy to understand this, thankyou Professor Dave!
great explanation appreciated a lot !!!! I understood now I couldn"t get it from the lectures.
I cannot express how much I want to thank you man
Unbelieveable! The most clear tutorial I've ever seen. Thanks!
Hell yeah gotta cram for my linear final tomorrow. Thanks for the refresh mate!
Just watched a 2 hour lecture. 6 min into this video I've learnt more , amazing and thank you sir
I'm trying to master eigens to code my algebraician level skill nodes in my Mentat project. Thanks, Dave!
Absolutely legendary video. Not a single sentence is wasted. Appreciate it
Always didn't understand this stuff but after watching your video it makes way more sense. Thanks
Very crystal clear explanation. Thank you.
Beautiful explanation, Thank you very much 🙏
Thank you Professor Dave your great work is much appreciated
My teacher for Linear algebra has a very confusing way of teaching, thank you so much for making it do simple
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.
Excellent explanation. Thanks for this
Thank you for this tutorial. Very easy to follow.
Great explanation.
This explanation helps in providing a clearer picture of the topic Thank you so much Sir 🙏🏻
You're the best, man! You make things seem so easy. Wish I meet you someday ❤
Thanks for helping me open my mind, you're better than my lecture at my university that i could easily get it
You have no idea how much you helped me. Thanks!❤
thanks professor. grateful from IIT, thanks for helping at the last moment of midsem exams. i have midsem exam in 3 hr.
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.
you are unbelievable
Thank you so much for this simple explanation
I wish you a great day, sir, im sure you've got many more video explanations like this on your channel.
Detailed and easy to understand，thank you
No words, thank you so much sir.
Great video with quality information, thank you.
I am glad to reach this illustration !!! Super Clear
You made it look so easy, Thank you so much 👌
This is genius.. i have no words!Thank you so much!!!
this man is always a lifesaver
Nice explanation. Thanks!
Good explanation, thank you!
You explained it clearly than my professor. Thank you!
Thank u so much sir for such a great explanation 🙏🏻 plz keep posting such videos
This is brilliant. Thank you!
Just took me minutes to realize how to find out eigenvectors. Thanks a lot
Thank you so much professor, u literally saved my day!
Thank you so much Sir.../\ You explain the topics way more easy for us to understand...
He knows a lot about this kind of stuff!
Only person alive who can explain maths clearly
Thanks for the great job done
16:46 I completely understand this topic now, thanks a lot
Great explanation!
Thank you so much professor dave
Thank you very much!Professor!
Amazing vid
Thank you Dave
You're amazing, thank you!
Man rly explained my 2hr lecture which I couldn't comprehend in 20 mins of which I now understand
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
Thank you so much 💗
Thank you for this video
The video has really helped me
Professor Dave you rock 😊
Perfect, just perfect!
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?
Thank you so much . You are the awesome teacher in the world. I wish you are also my school teacher
wow. Great Explanation
thank you so much for this !!
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.
Great explaination
Fantastic job sir👌
Thank you so much sir!!!!!
A subbed to you without thinking i really understood everything
THANK YOU SO MUCH!
@Professor Dave Explains may God bless you.
Thanks so much !