Good morning, Dr. Strang. It is always a pleasure to listen to your classes. I wish all classes were as well organized and thorough as yours. It is always a joy to listen to your classes.

MIT is MIT for a reason. Thank you for open sourcing such wonderful videos.

This is an outstanding lecture on Eigenvalues and Eigenvectors. Eigenvalues and Eigenvectors are very important for solving linear systems especially in differential equations. MIT and DR. Strang thank you so much.

Special is good. Useful is even better...

Thank you very much dear professor Strang. You have been saving and will save so many students.

22 minutes in, still waiting for the hard part; that's the genius of Gilbert Strang.

43:28 Strang sensei thinks student makes a mistake Strang sensei : *Death*

@yd9939

3 жыл бұрын

せんせい：定番なミスきちゃ！！

Love and appreciate Dr. Strang

Just one feedback from a student: It would be even better if the camera doesn't move too frequently following the lecturer. Thank you for all the camera works, just wanted to help make them even better. Thanks for great videos.

love the professor for clarity. I had no such a teacher in my college education

Great lesson from a humble Professor with a sense of humor.

I had this in my bachelor of computer science in german. My prof was way worse and he was talking in my language. I understand more this in english than my prof. In my language. Huge compliment to Dr.strang

Great lecture!!!Thank you Prof. Strang!

How lucky we are to have another wonderful Strang lecture! His insightful presentations are always a treat, and it's great to see his take on deep learning applications. Minor chalk-o: he rotated Ax the wrong way at 27:22 (but the math is still right)

@kellypainter7625

5 жыл бұрын

Even gods make mistakes.

@yorgunkaptaan

3 жыл бұрын

@@kellypainter7625 No.

Blessing to all peoples those are related to mathematics field

This man is a legend. Thanks for everything.

Brilliant, better insight than the original 18.06

@usmanhassan4498

2 жыл бұрын

Agreed

Thoroughly enjoyed Prof. Strang's lecture as usual (though it pains to see how aging has affected him!)

it's a very good course for someone to learn further on Matrixes in bachelor of Computer Science

In difference equation in 11:00 it is better to compare differential equation with v_t+1 - v_t =A* v_t.

Expecting to see Dr. Strang lecturing at age 106.

Way of solving ❤️

Impressed ❤️

@22:05 But how do we know B is invertable? I found a proof that does not assume B is invertable: Suppose we have x such that ABx = lambda * x. Left multiply both sides by B: BABx = lambda * Bx. This shows that Bx is an eigen vector of BA, and its eigen value is lambda.

28:00 Was it rotated to wrong direction? For example, if x = [0,1]^T, then AX = [1, 0]. So it is clockwise 90 degree rotation.

@learningstatistics1290

3 жыл бұрын

Yes, you are right. A good point.

Man! the camera guy has completely messed up such a beautiful lecture!

Will this course cover jacobian and hessian matrix?Just asking.

"vectors from the space formed by independent eigen vectors of original matrix A == eigen vectors themselves for some similar matrices to A (with same eigen values)"? Is this statement true or false? 42:24

@justpaulo

3 жыл бұрын

I think it's false. Here's why: A = X Λ X¯¹ B = M (X Λ X¯¹) M¯¹ = (M X) Λ (M X)¯¹ so the eigenvectors of B will be M X = [Mx1 Mx2 ... Mxn]. Each column of M X => Mx¡ is a linear combination of the columns of M, therefore it is in the column space of M ( C(M) ), but not necessarily in the column space of X. If the eigenvectors of B turned out to be XM, then they would be for sure in C(X), i.e. they would be a linear combination of the eigenvectors of A.

At 22:00 M = B only applies if B is invertible right? What about other cases when B isnt?

good teacher

10:56 - Could someone explain this? I didn't get the derivative.

@matthewearley3518

5 жыл бұрын

Check this link out: math.mit.edu/~jorloff/suppnotes/suppnotes03/la5.pdf He's making a overall comment on how eigenvectors are used to solve systems of linear differential (continuous-time) or difference (discrete-time) equations. It is one of their principal uses.

i wish they didnt move the cameras so much, i want to look at the blackboard, i don't mind if the professor is not in frame.

@igormorgado

3 жыл бұрын

you know that you can pause, right?

@adaelasm6467

Жыл бұрын

Yeah and then you aren’t hearing the professor talk about the equation

Are eigen vectors of a symmetric matrix already unit vectors, or we need to normalize them?

@zma4543

4 жыл бұрын

we need to normalize them to have length of 1 for each vector to get orthogonal matrix. I found this reference pretty good to answer your question in detail.

Solving ❤️

0:45 - We have heard about them eigentimes! ;)

I'm very thankful for these lectures. Though, the camera movement is sometimes annoying.

@seventyfive7597

4 жыл бұрын

Yep, the old camera angles, straight on and more static, were much more reasonable.

Is the equation in 22:00 written with matrices M and M inverse switched?

@elisad8372

3 жыл бұрын

yes I believe so

@Fan-vk8tl

3 жыл бұрын

both definitions is the same

22:00 25:20

Style ❤️

Golden hair ❤️

Duster ❤️

Handwriting ❤️

Way ❤️

Mic ❤️

Math ❤️

Board ❤️

Chalk ❤️

Accent ❤️

6:23 "that long, infinite series" hmmm....

@matthewearley3518

5 жыл бұрын

He is talking about a taylor series of e^(ax) e^ax = 1 + ax + (a^2)(x^2)/2! + (a^3)(x^3)/3! ... + (a^n)(x^n)/n! Since he has already proved that (A^n)*x=(lambda^n)*x, he just has to combine these two properties to prove that e^(Ax)=e^(lambda*x)

@marcusstoica

4 жыл бұрын

@@matthewearley3518 Thank you--saw the original comment before seeing the video, and came back down to answer it once I knew the context. Only thing I would add is that n -> +infinity.

Jazz ❤️

English ❤️

It`s kind of funny, the word "Eigenvector" is a mix of german with english

@thangible

3 жыл бұрын

except the german have the word vector too. Eigenvektor.

@hxqing

2 жыл бұрын

还好。我们不把它译为“爱根向量”，而译为“特征向量”。

@moritzstrueve5184

2 жыл бұрын

@@hxqing danke dir

20220517簽

oh God the distractions.

25:24 To prove AB and BA share the same eigenvalues, I think here the proof only proves the case when B is invertible. So this is not a general proof.

Never seen a worse camera man.

DEATH ... LOL

I'm the 951 viewer and 2nd commenter!!

Dr. Strange.

How these eigenvectors and eignvalues are Helpful In Industrial engineering field.....????

@o.y.930

4 жыл бұрын

u ever heard of google????

@rafiaumar7787

4 жыл бұрын

@@o.y.930 Yup i know ....Should I prefer GOOGLE to find the answer of this question??????¿¿¿

Unwatchable due to random unnecessary camera changes, such a shame. Seemed like it was gonna be an awesome lecture

Please stop taking the camera off the equations!!

stop panning the camera! stay on the balckboard