Singular Value Decomposition (the SVD)

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MIT RES.18-009 Learn Differential Equations: Up Close with Gilbert Strang and Cleve Moler, Fall 2015
View the complete course: ocw.mit.edu/RES-18-009F15
Instructor: Gilbert Strang
The SVD factors each matrix into an orthogonal matrix times a diagonal matrix (the singular value) times another orthogonal matrix: rotation times stretch times rotation.
License: Creative Commons BY-NC-SA
More information at ocw.mit.edu/terms
More courses at ocw.mit.edu

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5 май 2016

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Комментарии : 289

@qantum251 7 лет назад

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.

@salrite 6 лет назад

Agree... I can't imagine anyone can explain better

@Kneecap22 5 лет назад

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.

@gidi5779 4 года назад

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

@daniellavery6667 4 года назад

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.

@christophostertag4669 4 года назад

Shows no proof unfortuantely

@Sky-pg6xy Год назад

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.

@kiaraki7186 9 месяцев назад

its shit

@chrisjiang5121 4 года назад

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

@jironymojirolamus913 2 года назад

Came here while learning about PCA as well!

@Lil_sick0 11 месяцев назад

PCA bross

@H4nek 5 лет назад

3:35 "And what do I have? Well, I've got six matrices..." LOL

@handongfeng 2 года назад

No any other guys can teach algebra better than this Professor. He is the teacher's teacher, the best of the best. Respect!

@babaumar4188 4 года назад

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.

@jennariseley3161 5 лет назад

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!

@marcnassif2822 5 месяцев назад

For everyone else reading this, having a good grasp of Linear Algebra is absolutely essential for understanding Machine Learning!

@alexz5460 5 лет назад

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.

@shivamkak7981 9 месяцев назад

I have watched this several time over the course of the last year, and each time I have gained a deeper understanding. Thank you!

@gauravrudramalik5869 2 года назад

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!

@yaom9702 7 лет назад

I learn really a lot from your open lecture, thank you very much!!! prof Strang.

@GuruKal 8 лет назад

"eigenpeople...no, no, that's terrible"....lmaooo, too funny

@leetcoding1 5 лет назад

"eigenperson would be better"

@ayushgoel8277 5 лет назад

nice 1

@glarange72 5 лет назад

unique people, makes sense!

@8eodorosk 5 лет назад

there are the "eigenfaces" as well...

@juliocardenas4485 3 года назад

I’m with you

@lowerlowerhk 3 года назад

"how to I get hold of U?"- Gilbert Strang

@fmaleknia 7 лет назад

Best ever explanation I found on this topic. Now its going to clear. Thank you Prof.

@tomlee2065 4 года назад

I always enjoy watching Professor Strang’s lectures. I learnt a lot from them.

@psyduck1774 3 года назад

This lecture is an abosolute masterpiece. Thanks Prof. Strang.

@muhammadumaramanat738 3 года назад

In such a short video, finally know the relation between PCA and SVD.

@ahmadalghooneh2105 5 лет назад

Gilbert is the best, I love him, wish I had a teacher like that

@benhaze7468 3 года назад

This is so elaborately explained, yet so easy to understand This is what teaching should look like!

@azra8366 4 года назад

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 :)

@ABMMONIRUZZAMANKHAN 6 лет назад

great style of lecturing, always comes up discovering something. Thanks Prof. Gilbert Strang and MIT.

@zilezile4942 4 года назад

www.amazon.com/Data-Analysis-functional-principal-regression/dp/B088BM4FCB/ref=sr_1_5?dchild=1&keywords=NIZAR+Soilihi&qid=1589911627&sr=8-5

@sumedhdhale8553 3 года назад

I have great respect for this man, he's so devoted to his job.

@VenkataRamaRajuLolabhattu 6 лет назад

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

@pk_1320 7 лет назад

My favorite professor! Can't thank him enough ! THANK YOU for your teaching :)

@zilezile4942 4 года назад

www.amazon.com/Data-Analysis-functional-principal-regression/dp/B088BM4FCB/ref=sr_1_5?dchild=1&keywords=NIZAR+Soilihi&qid=1589911627&sr=8-5

@adamradekmartinez1536 6 лет назад

Very very clear explanation. Thank you very much Professor Strang.

@BalajiSankar Год назад

thank you for showing that SVD is actually getting the different layers of the matrix out .. from the most important to the least important..

@BetulGC 5 лет назад

Prof. Strang is absolutely the BEST!

@jjchen1010 8 лет назад

Thanks to Dr. Gilbert Strang!

@piaopiaokeke 7 лет назад

Gilbert Strang has aged like fine wine! We will have lost a real gem when he is gone. His teaching is amazing.

@ihbarddx 6 лет назад

Hey! Don't kill him off yet! I need him!

@diesel7777777 5 лет назад

I just can't wait to get to the age where people talking about say, "man, it's gonna suck when he dies."

@harineemosur6530 4 года назад

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!

@freeeagle6074 2 года назад

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.

@masteronepiece6559 5 лет назад

Finally some good content, I hate when a video is more than 30 minutes and full of garbage . But this video is gold

@mtp1376 4 года назад

Gilbert Strang is a genius on making difficult linear algebra topics understandable. I really appreciate his great work on being a powerful teacher.

@howmathematicianscreatemat9226 Год назад

😊

@univuniveral9713 4 года назад

When I was in Scandinavia, studying computer science, our textbook was by this same guru, Gilbert Strang. That book was pretty compact and perfect.

@shubhamdubey2283 5 лет назад

Hats off to you Sir. We are blessed to have people like you

@anahitasafari3094 7 лет назад

I could find art of teaching in this video... Thank you greatly....

@wiochan 3 месяца назад

This is the best SVD video on youtube

@livetolearn477 5 лет назад

I enjoy your lectures. Thanks respected Professor Dr. Gilbert Strang.

@salrite 6 лет назад

Awesome Lecture, the way he makes it so easy to digest, well detailed, thanks :)

@zhaochengliu9970 7 лет назад

Only 14 mins, solve all my problems!!! Thanks!

@sourovroy7951 4 года назад

Thanks Professor Gilbert and also Internet.

@kennarnett8220 5 лет назад

Thank you for teaching me the Linear Algebra I had to drop when I got mononucleosis. Now to pick up the Second Semester ....

@dhaneshprabhu4724 2 года назад

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

@amardda3489 5 лет назад

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.

@BackToBackSWE 4 года назад

you are loved

@gautamjain2487 6 лет назад

No words! just thank you prof.

@muhammadasaduzzaman7943 5 лет назад

Great lecture, Thank you, professor Strang.

@ShadowKMDu 8 лет назад

great video, clear illustration and explanation

@yimao2675 6 лет назад

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.

@zilezile4942 4 года назад

www.amazon.com/Data-Analysis-functional-principal-regression/dp/B088BM4FCB/ref=sr_1_5?dchild=1&keywords=NIZAR+Soilihi&qid=1589911627&sr=8-5

@gulrukhsor_akhmadjanova 3 месяца назад

just amazing professor and method of teaching, thank you a lot!

@companymen42 4 месяца назад

Dude dropping some sick knowledge bombs, blowing my mind.

@bierthai4436 8 лет назад

prime teacher, share knowledge to the world

@mostafaorooji5931 5 лет назад

Great Great Master. Whenever I get stuck in math, I would come here, I would find him and That's fine!

@austinwangler4700 4 года назад

Quality professor and lecture, this made SVD click for me

@pavanraickwade2124 3 года назад

Sir Gilbert Strang has this ability to convert boring theorems into lectures which are as interesting as movies...

@hailyabdelfattah4405 4 года назад

super course. We have his books in our university. Clear and simple.

@boomboom-dm6ip Год назад

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...

@sanjaykrish8719 7 лет назад

Best ever.. Superb Sir.. Thank you so much

@wandarinca 7 лет назад

I really like his algebra book!

@vctropdiamond 5 лет назад

One of the best introductory books on linear algebra, for sure

@kaerusemi Год назад

めちゃくちゃ分かりやすかった！！

@makingyouplacementready 4 года назад

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.

@anonymous-hl7ez 10 месяцев назад

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.

@tariqahassan5692 9 месяцев назад

You are the best professor ever ..

@ValeriaCalarco 3 года назад

Thank you so much for this incredible explanation! It added so much value to my day :)

@howmathematicianscreatemat9226 Год назад

😊

@nicholasmate 6 лет назад

Thank God for Gilbert Strang

@georgesadler7830 2 года назад

I am really learning linear algebra from one of the finest professor on earth.

@shahzad3518 5 лет назад

Salute to Great Sir Gilbert Strang

@jafarm4443 2 года назад

The number of time Prof. Strang saved me

@raymondlion314 6 лет назад

Mathematician is so cool.look at this guy, he almost know everything from finance to life science!

@adityakaushik8143 6 лет назад

This is awesome! Thank you so much Professor

@imalive404 6 лет назад

Sir I take a bow... Until now I didn't really understand SVD

@kamrupexpress 3 года назад

You are the God of linear algebra

@KayYesYouTuber 6 месяцев назад

You are a great professor. Thank you very much

@jakubmann3185 2 года назад

best video by the man who invented linear algebra, very cool

@dhruvgaba8516 4 года назад

Amazing! Thanks for such a nice explanation

@ibrahimatakankubilay9462 4 года назад

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!

@witness6347 9 месяцев назад

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.)

@phamtuan7106 6 лет назад

Great lecture! Thank you so much.

@anqiwen6997 4 года назад

Thanks, Professor, this lecture is nice.

@RC-bm9mf Год назад

Thanks a lot Prof Strang!

@flyingzipper 5 лет назад

Gilbert Strang is love... Gilbert Strang is life

@utkarshsanwal4908 3 года назад

Thanks, Sir. God Bless You Sir. You are exceptionally amazing.

@yodhakei 6 лет назад

Beautiful again

@MohitAwasthi01 2 года назад

Thanks a ton, Professor. ❤️

@tusharkantirouth5605 4 года назад

The ultimate guru of Linear Algebra...

@mipmap256 4 года назад

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.