Diagonalizing a Matrix

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
A matrix can be diagonalized if it has n independent eigenvectors. The diagonal matrix Λ is the eigenvalue matrix.
License: Creative Commons BY-NC-SA
More information at ocw.mit.edu/terms
More courses at ocw.mit.edu

[@JordanEdmundsEECS]

You have no idea how incredibly helpful those short little pauses to backtrack a little and clear things up are. Thank you.

[@kronikevaporation6007]

Thank youtube

[@maxramaswami4584]

Strang is the GOAT of linear algebra

[@tripp8833]

1.5x speed + Gilbert Strang = happiness

[@abdurrezzakefe5308]

Prof Strang is the best in Linear Algebra.

[@musikmakerfan]

MIT is lucky to have such a great lecturer.

[@jasonmarckx2912]

I"m in my first linear algebra course and am in awe of how immensely powerful this branch of mathematics is. MIT is fortunate to have a superb math teacher like Prof. Strang.

[@kunraiyan]

gotta appreciate how he said "I did that without preparing you for it", that was so humble.

[@georgesadler7830]

These mathematical tools are very important in science and engineering. Dr. Strang is an incredible human being for linear algebra.

[@donotwantahandle1111]

Came here to learn why diagonalizing a Hamiltonian is important and learnt from a real teacher!

[@MakerBen]

Thank heavens for this kind man :) More professors need to post high quality videos like this! This is super helpful! Thank you MIT!

[@TheAllen501]

Much better than my prof who always tries to explain some very simple concepts in the most complicated fancy way so that it might make him look more qualified. The best prof should explain complicated concepts in the easiest and most comprehensible manner as possible

[@alexandrefelicio3902]

THE BEST AND MOST PASSIONATE CLASSES I HAVE EVER WATCHED ON THE TOPIC

[@laurawitt8630]

I wish the professors at my university were this easy to understand!

[@adityagaykar]

Prof Gilbert Strang, thank you for the explanation. I bow to you _/\_

[@c0t556]

Aditya Gaykar I’m on my knees

[@siddharthsingi6772]

This still remains to be the best video explaining this stuff!

[@MsAlarman]

You are just a genius Gilbert! This is why you teach at MIT and wants to throw light on the shadows of ignorance in education round the globe. I am in bliss Sweet Angel!

[@malikialgeriankabyleswag4200]

So the column space of A or "transformed space by A" is the span of its eigenvectors! This makes sense of so many things you're the best Linear Algebra guy ever you legend

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Thank goodness for videos like these.

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what an absolute joy of sitting through a course taught by prof. strang.

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You're a great lecturer! :)

[@natalysalcedoguerra4078]

Thank you so much , excellent video.The best teacher that I ' ve seen until now.

[@musicalwanderings7380]

Thank you MIT OCW! Prof. Strang is the ultimate contributor to education! Thank you!!

[@pubgplayer1720]

Amazingly succinct and powerful - so much important stuff in just 10 minutes. Thanks prof strang.

[@tusharadevi538]

I just love Prof.Dr.Strang's passion for teaching. He is such an amazing teacher.
Having searched a lot of places to get an intuition about how different or same are eigen value decomposition and diagonalization of a matrix, voila, found all in one place. So glad to be learning concepts directly from a great mathematician like him.

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Tushara Devi again, Indians are everywhere 😀

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A Life time asset ❤ priceless gift by The sir Gilbert Strang

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I just love the lectures. You are the best sir. Kudos to you.

[@Raouli00]

I just had this in my lacture but didnt quite understand where the diagonal matrix came from but this cleared it up for me, thank you professor

[@LibertyAzad]

And this particular video was exceptionally helpful to me. Thank you!

[@Kneecap22]

Professor Gilbert Strang is the Stronkest at Linear Algebra! He is Lord King Captain General Warlord Supreme Commander of Linear Algebra!!!! Stronk!

[@HassanOmariprofile]

Thank you Dr. Strang, great video indeed

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Dear Prof, You are a fantastic teacher. Thank you very much.

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More than 80 years old, but taught better than the faculty of most Math schools in the world.

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a very good teacher.

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You are the best Prof Strang!Thank you!

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I let me go express my felling that you are the best Pr I have Seen.

[@saiveeryamahadevan1266]

Prof. Strang is AWESOME

[@yousafali7334]

First of all I would like to thank you sir for share your knowledge freely!I think it's wonderful for everyone who learn Multivariate analysis course....He/She must watch your videos.....Please share more of Calculus & other branch of mathematics...

[@tarlanahad]

Boss of Linear Algebra

[@shwang1579]

I can't believe that he can make this problem so easy for me to understand! Thx

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Reviewing for my final. Thank you so much for making it so easy.

[@AnkurDeka]

You are such a wonderful teacher!

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I just love you Professor.

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literally THE BEST TEACHER...

[@SL-cr3vh]

Understood very clearly, thank you very much! :)

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"That's very nice... that's very nice..."

[@flyingbirds6794]

that is a really absolutely wonderful video!!Thank you very much

[@minmaxwell]

I never thought about this before, but watching these videos, I began thinking: if I were to become a lecturer/professor one day, linear algebra and differential equations are definitely going to be courses I'd volunteer to teach.

[@infiniteprogramming6214]

This vid has made my life!

[@225discovery]

such a great explanations.

[@LuisGarcia-te5cr]

Thank you, very helpful explanation.

[@marcodong3749]

Oh damn, You enlightened me. Thank you very much!

[@maartenmtr3022]

great lecture thank you

[@noobody138]

What a great teacher!

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This is beautiful!

[@ihbarddx]

I suspect it helps that the lectures are aimed at engineers, rather than at mathematicians. For whatever reason, they are certainly wonderful.

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love this prof.

[@vinaykumardaivajna5260]

Super helpful and thank you so much

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we appriciate MIT and youtube for giving us our brain food
thanks proff gilbert strang
we also have herb gross for calculus

[@gogolgullu]

thanks gil

[@leixia6415]

A^n = V * L^n * V^(-1) is actually eigenvalue decomposition of n-th power of A. Mr. Strang's illustration on how taking powers && taking differentials are like moving discretely && continuously are very a novel idea to me

[@prateeksahni2923]

beautiful

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simply great

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makasih eyang strang :) jadi enak dan simple kalo bapak yang ngajar

[@sftekin4040]

This is beautiful...

[@emaniratnavalli3208]

Thank you so so much sir.

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Thank you.

[@hujiawei6774]

he makes linear algebra so beautiful to me

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Salute to you from Japan

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This guy is incredible

[@MrCigarro50]

Thank you

[@yanningli8362]

OH so clear!! Thanks a lot!

[@swagatodey4912]

Thank you thank you

[@bradypeng621]

Thank you sir

[@kencen4099]

It is so helpful.

[@sgzhou6242]

What a great mathematician!

[@bigboypal]

My Physics professors: *exhales in an annoyed fashion* "I really couldn't care less about the fact that I skipped 3 steps in my work while explaining a new concept this is extremely obvious and if you can't see it, I don't know how you made it into this class."
Gilbert Strang: "I did a matrix multiplication I didn't prepare you for. I'm really sorry."
Mr Strang I would literally die for you.

[@49853025]

thank. it help a lot

[@sanketgandhi3139]

Does V inverse always exist?

[@andrewl5267]

Do you get the same eigenvector multiple times when an eigenvalue has an algebraic multiplicity greater than one?

[@vikashdhanabal8984]

the best maths teacher in the universe including the ultragenius aliens in the space

[@KenRubenstein]

Gilbert is a good guy.....

[@dalisabe62]

This of course works only if V is a square matrix and non-singular; otherwise, inverse V does not exist and the entire technique crashes. On the other hand, the SVD decomposition works for all matrices even those that are singular, because the method incorporates the transpose in place of the inverse.

[@VFORVICTORY1000]

legend ,most of the tutorial didnt say the whole thing ,they just use the definition.

[@innocuousobservnt2325]

thanks

[@AbhishekJha-sz7cp]

both strang and mathematics are really cute

[@VinothKumar-qo7ry]

Thanks Lot sir

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Real Pro !

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Thanku MIT

[@MrParthmajumdar]

Awesome

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this is trippy

[@B.Shouvik17]

he is a legend.....
till 18-03-21
I was remembered that formula..........
GOD real GOD

[@deveshvaish8182]

So for any N X N matrix do we always have N eigenvalues and eigenvectors?

[@chrischris948]

If only all professors were half as good as Professor Strang.

[@Jinouga502]

"Eye"-gen vectors and "eye"-gen values.

[@sushantpoudel4372]

4:20 How can V have inverse? Isn't it a non square matrix?

[@Genshin_suit]

only the rocking star of linear algebra can do this

[@oudarjyasensarma4199]

ok I'm a little confused around 5:03
if we multiply both sides by v(inverse ) how are we getting v(inverse).A.V = "capital lambda(evm)"
we're supposed to get A = evm right?

[@infiniteprogramming6214]

We can't equalize v*lambda*vinv with v*vinv*lambda as matrix multiplication is not commutative

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11:19 Professor Strang gave us the secret to time travel

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If time travel was possible where are our guests from the future

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GOATbert Strang