Symmetric Matrices, Real Eigenvalues, Orthogonal Eigenvectors

MIT RES.18-009 Learn Differential Equations: Up Close with Gilbert Strang and Cleve Moler, Fall 2015
Instructor: Gilbert Strang

Symmetric matrices have n perpendicular eigenvectors and n real eigenvalues.

License: Creative Commons BY-NC-SA

[mirelladepietra]

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

[dalisabe]

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.

[mohammedal-haddad]

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

[saitaro]

Quality of explanation: Prof. Gilbert Strang

[georgesadler]

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

[pulkitatry]

Incridible 😮.... that's a time i truly enjoyed, every second was full of knowledge.Such a marvelous teacher ❤

[kamilazdybal]

Superb. Like all lectures of Professor Strang.

[wellingtonmusyoka]

Very elaborate and simple in explanation.

[siddhartharaja]

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

[jatinarora]

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

[gordito]

cosa bella, cosa hermosa, cosa bien hecha

[Diana-yljo]

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?

[allyourcode]

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...

[sourishsarkar]

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

[davidk]

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.

[aziz-dailycommentsandmore]

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