Diagonalizing a Matrix
ฝัง
- เผยแพร่เมื่อ 5 พ.ค. 2016
- 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
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You have no idea how incredibly helpful those short little pauses to backtrack a little and clear things up are. Thank you.
Thank youtube
Strang is the GOAT of linear algebra
Prof Strang is the best in Linear Algebra.
1.5x speed + Gilbert Strang = happiness
MIT is lucky to have such a great lecturer.
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.
gotta appreciate how he said "I did that without preparing you for it", that was so humble.
These mathematical tools are very important in science and engineering. Dr. Strang is an incredible human being for linear algebra.
Came here to learn why diagonalizing a Hamiltonian is important and learnt from a real teacher!
Thank heavens for this kind man :) More professors need to post high quality videos like this! This is super helpful! Thank you MIT!
I wish the professors at my university were this easy to understand!
Prof Gilbert Strang, thank you for the explanation. I bow to you _/\_
Aditya Gaykar I’m on my knees
This still remains to be the best video explaining this stuff!
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
THE BEST AND MOST PASSIONATE CLASSES I HAVE EVER WATCHED ON THE TOPIC
Amazingly succinct and powerful - so much important stuff in just 10 minutes. Thanks prof strang.
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!
Thank you Dr. Strang, great video indeed
And this particular video was exceptionally helpful to me. Thank you!
Thank you so much , excellent video.The best teacher that I ' ve seen until now.
what an absolute joy of sitting through a course taught by prof. strang.
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
Thank goodness for videos like these.
I just love the lectures. You are the best sir. Kudos to you.
Thank you MIT OCW! Prof. Strang is the ultimate contributor to education! Thank you!!
You're a great lecturer! :)
More than 80 years old, but taught better than the faculty of most Math schools in the world.
Dear Prof, You are a fantastic teacher. Thank you very much.
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
A Life time asset ❤ priceless gift by The sir Gilbert Strang
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.
Tushara Devi again, Indians are everywhere 😀
You are the best Prof Strang!Thank you!
Reviewing for my final. Thank you so much for making it so easy.
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...
a very good teacher.
Professor Gilbert Strang is the Stronkest at Linear Algebra! He is Lord King Captain General Warlord Supreme Commander of Linear Algebra!!!! Stronk!
Understood very clearly, thank you very much! :)
You are such a wonderful teacher!
I let me go express my felling that you are the best Pr I have Seen.
I can't believe that he can make this problem so easy for me to understand! Thx
Oh damn, You enlightened me. Thank you very much!
Prof. Strang is AWESOME
This is beautiful!
What a great teacher!
I just love you Professor.
such a great explanations.
great lecture thank you
that is a really absolutely wonderful video!!Thank you very much
love this prof.
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.
Thank you, very helpful explanation.
Boss of Linear Algebra
we appriciate MIT and youtube for giving us our brain food
thanks proff gilbert strang
we also have herb gross for calculus
This vid has made my life!
I suspect it helps that the lectures are aimed at engineers, rather than at mathematicians. For whatever reason, they are certainly wonderful.
thanks gil
literally THE BEST TEACHER...
"That's very nice... that's very nice..."
This is beautiful...
makasih eyang strang :) jadi enak dan simple kalo bapak yang ngajar
Super helpful and thank you so much
OH so clear!! Thanks a lot!
simply great
beautiful
Thank you so so much sir.
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
Thank you.
It is so helpful.
Salute to you from Japan
he makes linear algebra so beautiful to me
This guy is incredible
thank. it help a lot
Thank you sir
Thank you thank you
Thank you
What a great mathematician!
Gilbert is a good guy.....
Real Pro !
Thanku MIT
Thanks Lot sir
Awesome
Does V inverse always exist?
thanks
this is trippy
Do you get the same eigenvector multiple times when an eigenvalue has an algebraic multiplicity greater than one?
legend ,most of the tutorial didnt say the whole thing ,they just use the definition.
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.
the best maths teacher in the universe including the ultragenius aliens in the space
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.
If only all professors were half as good as Professor Strang.
he writes z just like my parents! shout out from really far away thankkkkkkks
both strang and mathematics are really cute
he is a legend.....
till 18-03-21
I was remembered that formula..........
GOD real GOD
Professor 🙏Love from india
So for any N X N matrix do we always have N eigenvalues and eigenvectors?
"Eye"-gen vectors and "eye"-gen values.
4:20 How can V have inverse? Isn't it a non square matrix?
GOATbert Strang
only the rocking star of linear algebra can do this
Each time you operate the same matrix on an eigenvector, you get back the same vector, just multiplied by its eigen value. So it's rather obvious that any n-th power of any matrix will have the same Eigen vectors, and Eigen values just get raised to the n-th power!