Singular Value Decomposition (the SVD)

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

[@Sky-pg6xy]

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]

its shit

[@chrisjiang5121]

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]

Came here while learning about PCA as well!

[@Lil_sick0]

PCA bross

[@babaumar4188]

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.

[@handongfeng]

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

[@jennariseley3161]

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]

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

[@qantum251]

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]

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

[@Kneecap22]

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]

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]

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]

Shows no proof unfortuantely

[@H4nek]

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

[@alexz5460]

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]

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]

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]

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

[@fmaleknia]

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

[@ABMMONIRUZZAMANKHAN]

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

[@zilezile4942]

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

[@VenkataRamaRajuLolabhattu]

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

[@ahmadalghooneh2105]

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

[@GuruKal]

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

[@leetcoding1]

"eigenperson would be better"

[@ayushgoel8277]

nice 1

[@glarange72]

unique people, makes sense!

[@8eodorosk]

there are the "eigenfaces" as well...

[@juliocardenas4485]

I’m with you

[@psyduck1774]

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

[@azra8366]

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 :)

[@benhaze7468]

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

[@tomlee2065]

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

[@adamradekmartinez1536]

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

[@lowerlowerhk]

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

[@pk_1320]

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

[@zilezile4942]

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

[@mtp1376]

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

[@howmathematicianscreatemat9226]

😊

[@sumedhdhale8553]

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

[@univuniveral9713]

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

[@jjchen1010]

Thanks to Dr. Gilbert Strang!

[@BetulGC]

Prof. Strang is absolutely the BEST!

[@yimao2675]

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]

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

[@livetolearn477]

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

[@kaerusemi]

めちゃくちゃ分かりやすかった！！

[@anahitasafari3094]

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

[@muhammadumaramanat738]

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

[@shubhamdubey2283]

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

[@kennarnett8220]

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

[@BalajiSankar]

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

[@salrite]

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

[@masteronepiece6559]

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

[@zhaochengliu9970]

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

[@amardda3489]

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.

[@piaopiaokeke]

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

[@ihbarddx]

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

[@diesel7777777]

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

[@harineemosur6530]

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]

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.

[@muhammadasaduzzaman7943]

Great lecture, Thank you, professor Strang.

[@gulrukhsor_akhmadjanova]

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

[@ShadowKMDu]

great video, clear illustration and explanation

[@wiochan]

This is the best SVD video on youtube

[@sourovroy7951]

Thanks Professor Gilbert and also Internet.

[@makingyouplacementready]

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]

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.

[@wandarinca]

I really like his algebra book!

[@vctropdiamond]

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

[@mostafaorooji5931]

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

[@pavanraickwade2124]

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

[@sanjaykrish8719]

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

[@gautamjain2487]

No words! just thank you prof.

[@Tyokok]

Hey does anyone understand why 13:50 "u1 is sort of combination of people, v1 is sort of combination of gene"? Thank you!

[@ValeriaCalarco]

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

[@howmathematicianscreatemat9226]

😊

[@companymen42]

Dude dropping some sick knowledge bombs, blowing my mind.

[@hailyabdelfattah4405]

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

[@bierthai4436]

prime teacher, share knowledge to the world

[@austinwangler4700]

Quality professor and lecture, this made SVD click for me

[@nicholasmate]

Thank God for Gilbert Strang

[@-salwa6276]

Why does the orthogonal matrix V physically represent (rotation) and sigma (stretching)? Thank you

[@georgesadler7830]

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

[@dhaneshprabhu4724]

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

[@raymondlion314]

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

[@adityakaushik8143]

This is awesome! Thank you so much Professor

[@dhruvgaba8516]

Amazing! Thanks for such a nice explanation

[@boomboom-dm6ip]

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...

[@imalive404]

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

[@phamtuan7106]

Great lecture! Thank you so much.

[@ibrahimatakankubilay9462]

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!

[@shreyaspakhare1313]

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.

[@markregev1651]

arent the eigenvalues for {2,2}{1,1} 0 and 3?

[@shahzad3518]

Salute to Great Sir Gilbert Strang

[@KayYesYouTuber]

You are a great professor. Thank you very much

[@jafarm4443]

The number of time Prof. Strang saved me

[@pedroluisalcazar9285]

Thanks Mr Gilbert, you Rock!,

[@BackToBackSWE]

you are loved

[@jakubmann3185]

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

[@anqiwen6997]

Thanks, Professor, this lecture is nice.

[@tariqahassan5692]

You are the best professor ever ..

[@utkarshsanwal4908]

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

[@RC-bm9mf]

Thanks a lot Prof Strang!

[@MohitAwasthi01]

Thanks a ton, Professor. ❤️

[@amosbationo4653]

Interesting examples with applied statistics.Thanks Sir.

[@ritaprasad438]

Good explanations

[@tusharkantirouth5605]

The ultimate guru of Linear Algebra...

[@prabalghosh2954]

thanks for this lecture

[@juliocardenas4485]

Wonderfully explained

[@kaanyolsever1149]

I love this prof hahaha. Hilarious and amazing lecture

[@karius85]

Great lesson!

[@flyingzipper]

Gilbert Strang is love... Gilbert Strang is life

[@soodabeh880]

amazing ; thank you prof

[@chaoruizhe]

Great video!

[@learningsuper6785]

Such a great man!

[@LionelGuglielmone]

Amazing, AGAIN!

[@kamrupexpress]

You are the God of linear algebra

[@sachintelang6449]

Thank you Sir. Best Regards

[@yodhakei]

Beautiful again

[@witness6347]

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.)

[@muhittinselcukgoksu1327]

Thank you sooo much ,Sir.

[@user-wr4yl7tx3w]

Amazing content