I can’t express how amazing this video is. I have taught from a number of textbooks in different undergrad linear algebra classes, and I’ve never in my life seen an explanation of SVD as good as this one.
I used to watch Prof. Strang's videos when I was a first year undergrad. Never thought I would revisit this during my master as I am learning about PCA... Time flies yet Prof. Strang is forever
With all due respect, on which basis people did thumbs down this outstanding piece of algebra. If I had Profs. like Sir Gibert Strang at my early university years, I would've reached far beyond my own expectations. Your teaching is outstandingly straightforward Sir.
I could imagine mathematics students to be dissatisfied by the lack of rigour. Are we talking about the standard inner product w.r.t. “orthogonal”? Over what field is the matrix? Is it even a field? How about existence and uniqueness of SVD? Etc. As a video explaining the procedure it’s very fine, but as opposed to engineers, that’s not necessarily what mathematicians are looking for in a video on SVD
Perhaps because he buries the lede with the intention and applications towards the end, and the only "worked example" excludes all the procedure for actually computing the component matrices. Then the discussion of applications is, frankly, pretty disorganized. Gilbert Strang has written some good books in his day, and even has some good lecture videos on youtube, but this is not a great example of his teaching.
I have been trying to understand PCA all semester. I didn't realise that I would finally 'get' it after watching this video on SVD. Thank you so much Dr Strang and MIT!
eigen people (or person) is the one of the greatest examples by Proff. Gilbert Strang. This one statement cleared many questions about PCA. Can't thank him enough, great professor. Thank you
When I learnt linear algebra in college, I couldn't understand why I need to learn it besides it was required. Profs Gibert Strange made it more meaningful and helped me understand its application in practice. All the pieces I learnt are now connected.
I don't want him to die. The passion he has for teaching at that age is amazing.I have had profs in college who hated teaching basics and then I see this gentleman put so much effort in teaching same.Great man!
Professor Arthur Mattuck, one of early pop stars of DE, passed away last year at age 91. Professor Herbert Gross, kindof the earliest calculus star, also passed away a few years ago. Pray that Professor Strang will live a long long long life.
This prof is just amazing. In our college, only the formula and a large sequence of steps were mentioned to find SVD. I had a hard time comprehending it. This legend just mad eme understand SVD in just 2 equations with full concept. I wish I was born next to MIT. Thanku prof for enlightening me. And Thanku MIT OCW for making these vdos available
Thank you so much Prof. Strang, and sincere gratitude towards MIT for an initiative like the OCW. Blessed are those who have the motivation to develop their skills in their younger years, and make it to an institution like MIT... but yeah, with uploads like this... even people like me can continue to develop our knowledge and understanding. I am so glad and grateful to have an opportunity like this!
I studied all this in small pieces, matrix in class 9th, Singular Matrix Decomposition in M.Tech. and Principle Component Analysis during my research in Speech Recognition using ANN. This video shows correlation in an exemplary manner. Best part is ...it sounds so simple and obvious. That's the trait of a teacher par excellence.
I have always liked his explanations but I just learnt his name today from the comments. It was familiar name. And when I sat down with my Linear Algebra book I saw it. Wow... He is a legend huh...
All of my life I looked for the singular vector corresponding to the smallest singular value to solve linear systems. And now I learn that the biggest value is the most important one.
I first watched Mr Strang lesson in 2003. Which helped me found a good job in Special effects industry. Used a lot of matrix transform and FEM physical simulation. Can not thank him enough.
6:12 Prof says "A^TA and AA^T have the same eigenvalues", which is partially true. It should be amended as: A^TA and AA^T have the same set of NON-Zero eigenvalues. In the case of A is rectangular, it might happen that AA^T has a zero eigenvalue but A^TA doesn't. (or A^TA has a zero eigenvalue but AA^T doesn't.)
The vector U at 8.56 is incorrect. The one he wrote on the board is uT (2,1,-1,2). It should have been just U (2,-1,1,2). You can try multiplying all pieces on the right side, and it is not equal to the left side.
I guess he could have used the original matrixes and He should have left the -ve on the second row entry of the unit U matrix alone and it would be fine considering he choose -1 as a free variable in the second column for x2.However,he was moving so fast to have time for corrections.
Due to technical difficulties, I was once forced to teach a class on a chalkboard. Worst experience of my career. Boggles my mind that "at the most prestigious technical college in the whole f***in' world" (yes, I just quoted Good Will Hunting), they still use them. Regardless, though, the teaching is great, and that's what really matters.
7:30 I think Prof Gilbert make a mistake in U matrix, U should be [ 2 -1 | 1 2 ] and not [ 2 1 | -1 2 ] as shown in the video, the matrix in video is actually U^T and not U.
I think the (2,1) for the first column and (-1,2) for the second column and then multiplied by 1/sqrt(5). He probably chose -1 as a free variable for x2 for the second column of the V matrix. I guess the free variables can make them look identical but of different signs.
Great Lecture by Prof Strang ! Could anyone explain why he mentions that the matrix has rank one at 12:38 and how he concludes that the singular value sigma is what is selling us ? Thanking you in anticipation.
Thanks Prof. Strang and MIT. This is the second course I do with prof. Strang here in youtube, and I am starting the third soon :). Just one comment for everybody, please check again the eigenvectors for the (A A^T) matrix in this video. For the evalue of 10, the evector would be (2 1), and for the evalue of 0 would be (1 -2), written as columns. Am I right?
Eigenvectors are the same even if they are multiplied by a scalar. So in the Professor's case, his eigenvectors are multiplied by a scalar -1 compared to yours. Both of your eigenvectors yield the same results.
I can’t express how amazing this video is. I have taught from a number of textbooks in different undergrad linear algebra classes, and I’ve never in my life seen an explanation of SVD as good as this one.
its shit
I used to watch Prof. Strang's videos when I was a first year undergrad. Never thought I would revisit this during my master as I am learning about PCA... Time flies yet Prof. Strang is forever
Came here while learning about PCA as well!
PCA bross
No any other guys can teach algebra better than this Professor. He is the teacher's teacher, the best of the best. Respect!
With all due respect, on which basis people did thumbs down this outstanding piece of algebra. If I had Profs. like Sir Gibert Strang at my early university years, I would've reached far beyond my own expectations. Your teaching is outstandingly straightforward Sir.
Agree... I can't imagine anyone can explain better
I think they haven't seen 18.06, the best course on linear algebra! They need to see lecture 25, 28 and 29. Before this one.
I could imagine mathematics students to be dissatisfied by the lack of rigour. Are we talking about the standard inner product w.r.t. “orthogonal”? Over what field is the matrix? Is it even a field? How about existence and uniqueness of SVD? Etc. As a video explaining the procedure it’s very fine, but as opposed to engineers, that’s not necessarily what mathematicians are looking for in a video on SVD
Perhaps because he buries the lede with the intention and applications towards the end, and the only "worked example" excludes all the procedure for actually computing the component matrices. Then the discussion of applications is, frankly, pretty disorganized. Gilbert Strang has written some good books in his day, and even has some good lecture videos on youtube, but this is not a great example of his teaching.
Shows no proof unfortuantely
The best linear algebra by all standards. He makes it look so simple. This explanation of SVD and PCA blew my mind. I salute you prof.
I have been trying to understand PCA all semester. I didn't realise that I would finally 'get' it after watching this video on SVD. Thank you so much Dr Strang and MIT!
For everyone else reading this, having a good grasp of Linear Algebra is absolutely essential for understanding Machine Learning!
Gilbert Strang is a genius on making difficult linear algebra topics understandable. I really appreciate his great work on being a powerful teacher.
😊
eigen people (or person) is the one of the greatest examples by Proff. Gilbert Strang. This one statement cleared many questions about PCA. Can't thank him enough, great professor. Thank you
Each time, when I have the question about algebra, I always come to look for the answer in these lessons of Prof Gilbert. Thank you, Prof Gilbert.
I have watched this several time over the course of the last year, and each time I have gained a deeper understanding. Thank you!
When I learnt linear algebra in college, I couldn't understand why I need to learn it besides it was required. Profs Gibert Strange made it more meaningful and helped me understand its application in practice. All the pieces I learnt are now connected.
www.amazon.com/Data-Analysis-functional-principal-regression/dp/B088BM4FCB/ref=sr_1_5?dchild=1&keywords=NIZAR+Soilihi&qid=1589911627&sr=8-5
Gilbert Strang has aged like fine wine! We will have lost a real gem when he is gone. His teaching is amazing.
Hey! Don't kill him off yet! I need him!
I just can't wait to get to the age where people talking about say, "man, it's gonna suck when he dies."
I don't want him to die. The passion he has for teaching at that age is amazing.I have had profs in college who hated teaching basics and then I see this gentleman put so much effort in teaching same.Great man!
Professor Arthur Mattuck, one of early pop stars of DE, passed away last year at age 91. Professor Herbert Gross, kindof the earliest calculus star, also passed away a few years ago. Pray that Professor Strang will live a long long long life.
"how to I get hold of U?"- Gilbert Strang
Gilbert is the best, I love him, wish I had a teacher like that
This is so elaborately explained, yet so easy to understand
This is what teaching should look like!
3:35 "And what do I have? Well, I've got six matrices..." LOL
When I was in Scandinavia, studying computer science, our textbook was by this same guru, Gilbert Strang. That book was pretty compact and perfect.
This prof is just amazing. In our college, only the formula and a large sequence of steps were mentioned to find SVD. I had a hard time comprehending it. This legend just mad eme understand SVD in just 2 equations with full concept. I wish I was born next to MIT. Thanku prof for enlightening me. And Thanku MIT OCW for making these vdos available
thank you for showing that SVD is actually getting the different layers of the matrix out .. from the most important to the least important..
Best ever explanation I found on this topic. Now its going to clear. Thank you Prof.
Thank you so much Prof. Strang, and sincere gratitude towards MIT for an initiative like the OCW.
Blessed are those who have the motivation to develop their skills in their younger years, and make it to an institution like MIT... but yeah, with uploads like this... even people like me can continue to develop our knowledge and understanding.
I am so glad and grateful to have an opportunity like this!
In such a short video, finally know the relation between PCA and SVD.
Finally some good content, I hate when a video is more than 30 minutes and full of garbage . But this video is gold
Rotate Stretch rotate can't be explained more simply thank you
I studied all this in small pieces, matrix in class 9th, Singular Matrix Decomposition in M.Tech. and Principle Component Analysis during my research in Speech Recognition using ANN. This video shows correlation in an exemplary manner. Best part is ...it sounds so simple and obvious. That's the trait of a teacher par excellence.
Is research in AI ML valued in industry in India? I'm a final year engineering student wondering whether to focus a lot on research.
I have great respect for this man, he's so devoted to his job.
I learn really a lot from your open lecture, thank you very much!!! prof Strang.
I have always liked his explanations but I just learnt his name today from the comments. It was familiar name. And when I sat down with my Linear Algebra book I saw it. Wow... He is a legend huh...
This lecture is an abosolute masterpiece. Thanks Prof. Strang.
great style of lecturing, always comes up discovering something. Thanks Prof. Gilbert Strang and MIT.
www.amazon.com/Data-Analysis-functional-principal-regression/dp/B088BM4FCB/ref=sr_1_5?dchild=1&keywords=NIZAR+Soilihi&qid=1589911627&sr=8-5
"eigenpeople...no, no, that's terrible"....lmaooo, too funny
"eigenperson would be better"
nice 1
unique people, makes sense!
there are the "eigenfaces" as well...
I’m with you
Prof. Strang is absolutely the BEST!
Sir Gilbert Strang has this ability to convert boring theorems into lectures which are as interesting as movies...
This is the best SVD video on youtube
The number of time Prof. Strang saved me
I really like his algebra book!
One of the best introductory books on linear algebra, for sure
All of my life I looked for the singular vector corresponding to the smallest singular value to solve linear systems. And now I learn that the biggest value is the most important one.
I first watched Mr Strang lesson in 2003. Which helped me found a good job in Special effects industry. Used a lot of matrix transform and FEM physical simulation. Can not thank him enough.
I am really learning linear algebra from one of the finest professor on earth.
I could find art of teaching in this video...
Thank you greatly....
6:12 Prof says "A^TA and AA^T have the same eigenvalues", which is partially true. It should be amended as:
A^TA and AA^T have the same set of NON-Zero eigenvalues.
In the case of A is rectangular, it might happen that AA^T has a zero eigenvalue but A^TA doesn't. (or A^TA has a zero eigenvalue but AA^T doesn't.)
I always enjoy watching Professor Strang’s lectures. I learnt a lot from them.
The first in the world to actually explain very well wtf is this SVD
I thought the SVD was a sniper rifle.
www.amazon.com/Data-Analysis-functional-principal-regression/dp/B088BM4FCB/ref=sr_1_5?dchild=1&keywords=NIZAR+Soilihi&qid=1589911627&sr=8-5
it kinda is: PCA
I thought it was marihuana
That's SVG brudda
it is. it is made in USSR.
The vector U at 8.56 is incorrect. The one he wrote on the board is uT (2,1,-1,2). It should have been just U (2,-1,1,2). You can try multiplying all pieces on the right side, and it is not equal to the left side.
You are right, the multiplication of the right part is [[ 2. 2.],[-1. -1.]], different from the original A
Thanks to Dr. Gilbert Strang!
Thank u for explaining us the application, It's a huge motivation for learning such stuff.
I wish I had a teacher like you prof Strang :)
My favorite professor! Can't thank him enough ! THANK YOU for your teaching :)
www.amazon.com/Data-Analysis-functional-principal-regression/dp/B088BM4FCB/ref=sr_1_5?dchild=1&keywords=NIZAR+Soilihi&qid=1589911627&sr=8-5
You are the God of linear algebra
best video by the man who invented linear algebra, very cool
Hats off to you Sir. We are blessed to have people like you
Quality professor and lecture, this made SVD click for me
The ultimate guru of Linear Algebra...
just amazing professor and method of teaching, thank you a lot!
Mathematician is so cool.look at this guy, he almost know everything from finance to life science!
super course. We have his books in our university. Clear and simple.
Thanks Professor Gilbert and also Internet.
Very very clear explanation. Thank you very much Professor Strang.
I enjoy your lectures. Thanks respected Professor Dr. Gilbert Strang.
Sir I take a bow... Until now I didn't really understand SVD
Dude dropping some sick knowledge bombs, blowing my mind.
You are the best professor ever ..
Only 14 mins, solve all my problems!!! Thanks!
Loved it. I doubt they lecture so simple and clear in real courses though. I doubt they add quite a bit more depth-and board space!
you are loved
Very good lecture. A in the last example should be [2, 2; -1, -1]
I guess he could have used the original matrixes and He should have left the -ve on the second row entry of the unit U matrix alone and it would be fine considering he choose -1 as a free variable in the second column for x2.However,he was moving so fast to have time for corrections.
You nailed SVD
I understand now it more clearly
めちゃくちゃ分かりやすかった！！
Thank you for teaching me the Linear Algebra I had to drop when I got mononucleosis. Now to pick up the Second Semester ....
Best ever.. Superb Sir.. Thank you so much
Thank God for Gilbert Strang
Gilbert Strang is love... Gilbert Strang is life
Watch 18.06 lecture 25, 28 and 29; before watching this one.
You are a great professor. Thank you very much
5:32
you already had my attention
and now you have my love
Due to technical difficulties, I was once forced to teach a class on a chalkboard. Worst experience of my career. Boggles my mind that "at the most prestigious technical college in the whole f***in' world" (yes, I just quoted Good Will Hunting), they still use them.
Regardless, though, the teaching is great, and that's what really matters.
7:30 I think Prof Gilbert make a mistake in U matrix, U should be [ 2 -1 | 1 2 ] and not [ 2 1 | -1 2 ] as shown in the video, the matrix in video is actually U^T and not U.
No words! just thank you prof.
"I'm having a lot of fun here with transposes..."
prime teacher, share knowledge to the world
I was itching towards the end for him to name drop Jacobian matrices
Oh! Tricky Mr. Strang took square matrix 2 by 2 as example.
I think the (2,1) for the first column and (-1,2) for the second column and then multiplied by 1/sqrt(5). He probably chose -1 as a free variable for x2 for the second column of the V matrix. I guess the free variables can make them look identical but of different signs.
Great Great Master. Whenever I get stuck in math, I would come here, I would find him and That's fine!
Salute to Great Sir Gilbert Strang
great video, clear illustration and explanation
I go to berkeley and this dude still explains it better lmfao
The heart of SVD is here !
Wow great explanation no waste of time.
A small typo of the example, the matrix A should be [[2 2], [-1 -1]], or the -1 in u be swapped.
Great Lecture by Prof Strang ! Could anyone explain why he mentions that the matrix has rank one at 12:38 and how he concludes that the singular value sigma is what is selling us ? Thanking you in anticipation.
Awesome Lecture, the way he makes it so easy to digest, well detailed, thanks :)
Thanks, Sir. God Bless You Sir. You are exceptionally amazing.
He is the Mr. Rogers of math.
Thanks Prof. Strang and MIT. This is the second course I do with prof. Strang here in youtube, and I am starting the third soon :).
Just one comment for everybody, please check again the eigenvectors for the (A A^T) matrix in this video. For the evalue of 10, the evector would be (2 1), and for the evalue of 0 would be (1 -2), written as columns. Am I right?
i got the same result as you did :) either I got something wrong with my understanding of eigenvectors or he made a mistake.
I think he meant to have [-1, -1] as the lower row in his A matrix.
Eigenvectors are the same even if they are multiplied by a scalar. So in the Professor's case, his eigenvectors are multiplied by a scalar -1 compared to yours. Both of your eigenvectors yield the same results.
the prof. is excellent
Thanks Mr Gilbert, you Rock!,
arent the eigenvalues for {2,2}{1,1} 0 and 3?
In 2020, every single cat video has more than 1M views, yet a free lecture from an MIT professor has only 300K.
Thank you so much for this incredible explanation! It added so much value to my day :)
😊