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.
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!
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
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 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...
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 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.
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.
I too had my dad leave me and from a young age, many of my actions have been interpreted as compensating for not having a male figure in my life lead me and guide me and to look up too. Prof Strang is tight.
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.
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.
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.
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
No any other guys can teach algebra better than this Professor. He is the teacher's teacher, the best of the best. Respect!
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
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.
😊
3:35 "And what do I have? Well, I've got six matrices..." LOL
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.
Finally some good content, I hate when a video is more than 30 minutes and full of garbage . But this video is gold
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.
Gilbert is the best, I love him, wish I had a teacher like that
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 have watched this several time over the course of the last year, and each time I have gained a deeper understanding. Thank you!
This is so elaborately explained, yet so easy to understand
This is what teaching should look like!
When I was in Scandinavia, studying computer science, our textbook was by this same guru, Gilbert Strang. That book was pretty compact and perfect.
thank you for showing that SVD is actually getting the different layers of the matrix out .. from the most important to the least important..
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
"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
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.
Best ever explanation I found on this topic. Now its going to clear. Thank you Prof.
This is the best SVD video on youtube
Sir Gilbert Strang has this ability to convert boring theorems into lectures which are as interesting as movies...
In such a short video, finally know the relation between PCA and SVD.
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...
"how to I get hold of U?"- Gilbert Strang
This lecture is an abosolute masterpiece. Thanks Prof. Strang.
I really like his algebra book!
One of the best introductory books on linear algebra, for sure
Prof. Strang is absolutely the BEST!
I am really learning linear algebra from one of the finest professor on earth.
Sir I take a bow... Until now I didn't really understand SVD
I could find art of teaching in this video...
Thank you greatly....
The number of time Prof. Strang saved me
The first in the world to actually explain very well wtf is this SVD
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.)
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
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
best video by the man who invented linear algebra, very cool
The ultimate guru of Linear Algebra...
Thanks to Dr. Gilbert Strang!
Rotate Stretch rotate can't be explained more simply thank you
Only 14 mins, solve all my problems!!! Thanks!
You are the God of linear algebra
I always enjoy watching Professor Strang’s lectures. I learnt a lot from them.
Thank God for Gilbert Strang
Gilbert Strang is love... Gilbert Strang is life
Mathematician is so cool.look at this guy, he almost know everything from finance to life science!
Hats off to you Sir. We are blessed to have people like you
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 :)
Quality professor and lecture, this made SVD click for me
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
you are loved
Very very clear explanation. Thank you very much Professor Strang.
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.
5:20 "..that tells me V, that tells me sigma, ... AND *YOU* DISAPPEARED here. " LOL
Best ever.. Superb Sir.. Thank you so much
Thanks Professor Gilbert and also Internet.
You are the best professor ever ..
The heart of SVD is here !
Dude dropping some sick knowledge bombs, blowing my mind.
super course. We have his books in our university. Clear and simple.
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.
just amazing professor and method of teaching, thank you a lot!
Thank you for teaching me the Linear Algebra I had to drop when I got mononucleosis. Now to pick up the Second Semester ....
I enjoy your lectures. Thanks respected Professor Dr. Gilbert Strang.
You nailed SVD
I understand now it more clearly
In 2020, every single cat video has more than 1M views, yet a free lecture from an MIT professor has only 300K.
prime teacher, share knowledge to the world
めちゃくちゃ分かりやすかった！！
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
No words! just thank you prof.
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.
You are a great professor. Thank you very much
I want him to adopt me.
I'm lucky enough, to have a dad just like that. Former University professor. Even today, approaching 80 years old, he still tells me such stories.
#me2
@@jeanr2571 please hire me your Father to be our father to teach me some pure mathematics. Am serious.
I too had my dad leave me and from a young age, many of my actions have been interpreted as compensating for not having a male figure in my life lead me and guide me and to look up too.
Prof Strang is tight.
tamam
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!
Watch 18.06 lecture 25, 28 and 29; before watching this one.
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.
5:32
you already had my attention
and now you have my love
I go to berkeley and this dude still explains it better lmfao
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.
great video, clear illustration and explanation
"I'm having a lot of fun here with transposes..."
He is the Mr. Rogers of math.
the prof. is excellent
Oh! Tricky Mr. Strang took square matrix 2 by 2 as example.
Thanks, Sir. God Bless You Sir. You are exceptionally amazing.
Thank you so much for this incredible explanation! It added so much value to my day :)
😊
Wow great explanation no waste of time.
Awesome Lecture, the way he makes it so easy to digest, well detailed, thanks :)
Thanks Mr Gilbert, you Rock!,
Great lecture, Thank you, professor Strang.
Thanks a lot Prof Strang!
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.
Wonderfully explained