Simply the best. How much passion in this man?how much charisma, knowledge power and skills???this is awesome,mesmerizing.

the minute you think you got bored watching him, he will hit you with a dose of refreshing challenge. He never swamps you with theory to the point of losing touch with reality, but he uses simple examples to extrapolate theory very quickly. Amazing lecturer who mastered his material yet never got tired of presenting it to different crowds.

Professor Strang, every lecture of yours is like a symphony to me. Thank you very much.

Quality of explanation: Prof. Gilbert Strang

Superb. Like all lectures of Professor Strang.

This is linear algebra at its finest. Dr. Strang you are a linear algebra legend.

Thank you Professor.

Very elaborate and simple in explanation.

wonderful lecture by prof gilbert strang. Like the way he taught made it easy

@2:22 is my favorite part!

Just wants to thanks,only because this content is free!!

This man is a legend

very well done

Pure gold..

nice working

As he said at 4:12 the trace is 6 and determinant is 8, so the eigenvalues 2and4 is correct. Can anyone plz tell me what and why they have such relationship?

@gainauntu

5 жыл бұрын

det of that marix = 8 which should be equal to the product of eigenvalues which is 4*2=8.....since one the eigenvalue is 2...another on should be trace(MATRIX)-2=6-2=4

@valeriapedrosa7964

5 жыл бұрын

Because the Characteristic Equation of a Matrix A (2X2 ) is : P(x)= x^2 - trace(A)x + det(A)

cosa bella , cosa hermosa , cosa bien hecha

@alejandroencinas2905

5 жыл бұрын

What is this guy talking about?, idk but this video was amazing!!

the Passion!!!

What if I have a symmetric matrix with repeated eigenvalues? Will the eigenvectors will always be orthogonal?

@nickirpdark

7 жыл бұрын

No, orthogonality only happens if the eigenvalues are different. For the case of repeated eigenvalues your space is degenerate.

@sourishsarkar5281

7 жыл бұрын

Nicolas .Pacheco Please refer to the book by Gilbert Strang which I came across recently, where he has proved by mathematical induction that the eigenvectors of a symmetric matrix will be orthogonal even if the eigenvalues are repeated..

@nickirpdark

7 жыл бұрын

which one, Introduction to Linear Algebra or Linear Algebra and Its Applications? and if it's not too much trouble can you remember the chapter.

@sourishsarkar5281

7 жыл бұрын

Introduction to linear algebra. I have the fourth edition. There, it is explained in chapter 6: Eigenvalues and Eigenvectors in section 6.4: Symmetric matrices.

@nickirpdark

7 жыл бұрын

The ideia here is that for symmetric matrices you can choose a suitable orthonormal basis that generates the eigenvector space., such that you can diagonalize the matrix The thing with repeated eigenvalues in symmetric matrices is that you have an eigenvector space of dimension n, where n is the multiplicity of of the eigenvalue, so it's possible for you to choose an pair eigenvectors that are not necesserally orthogonal.

Oh, I landed at the right video.

👑

Isn't B an antisymmetric matrix? Doesn't that mean that the eigenvalues are supposed to be imaginary? But according to Professor Strang's calculation, the eigenvalues are 3 + i and 3 - i, which are not imaginary...

@iteoluwaoladejo4240

Жыл бұрын

B is not antisymmetric.

@mlabodia

7 ай бұрын

Why not?

Prooooooof please

What is an orthogonal matrix?

@ajarivas72

Жыл бұрын

A is orthogonal matrix if Transpose(A) = A and determinant(A) = 1

@AchtungBaby77

7 ай бұрын

@@ajarivas72 An easier way to define an orthogonal matrix is that its transpose is its inverse.

@ajarivas72

6 ай бұрын

@@AchtungBaby77 You are correct. I made a mistake in my response. Transpose(A) = inv(A)

It breaks my heart to say it, but this man needs to be put to sleep - he is *clearly* struggling and suffering. He absolutely is a national treasure and should forever be remembered as such, but it is time to give this man the dignified - and much overdue - outro that he so rightfully deserves and desperately needs.

@owzok7087

6 ай бұрын

?????

ah I see, no men of culture here, excuse me