Eigenvalues and Eigenvectors

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

The eigenvectors remain in the same direction when multiplied by the matrix. Subtracting an eigenvalue from the diagonal leaves a singular matrix: determinant zero. An n by n matrix has n eigenvalues.

License: Creative Commons BY-NC-SA

[reneeliu]

I wish I could someday bump into Dr. Strang in a supermarket because I want to salute to him.
A while back when I was learning algebra in college, I was paying tuition to my own professor (didn't learn anything from him) while learning everything from Dr.Strang's older videos for free. I am very grateful until this day and always will be.

[kiichit]

Love those lectures that begin with why you need it

[milkdrinker]

I just learned more in 10 minutes of you than I've learned in the last 2 weeks of lectures

[zainuddinkhan]

sir i have never seen a better mathematician than you.

[umutguvercin]

The reason why i love linear algebra is you Sir. Enthusiasm to teach is the most important thing a lecturer should have, and i am glad the say that you have enough for thousands of students. :)

[georgesadler]

These are powerful linear algebra concepts. Linear algebra is a power tool in signal and systems theory, which is a part of the electrical engineering program. When I took this class at the University of Maryland College Park years ago there was a little emphasis on linear algebra. Dr. Strang thank you so much for your contribution to the subject.

[naf]

Professor I have an infinite admiration for your clarity and precision of your mind. Your lessons are unequalled. Thank you so much.

[rajvinderkaur]

thanks alot sir. i dont know how can i pay gratitude to u.. Thanks to the MIT. great appreciation.

[SparkyElectricDave]

History for generations will remember your good work, just love it.

[mustafasoylemezo]

İ think his explanation is so clear and fluent.İ like his lectures very much and i appreciate him.

[Ggnera]

Prof. Strang is excellent at teaching! The video was very useful. Thank you!

[rutika]

Sir you are awesome.
Can't find a better teacher than u.
Thanks a lot for all your efforts.

[erion]

That was a gold lecture, in 19:00 minutes i learn what my teacher was trying to tell 4 lessons!!!

[FloppyDobbys]

It makes intuitive sense that the Eigen vector remains the same with A^n because we can see A^n as just applying the same transformation n times. Applying the same n times doesn't change the direction of the eigen vectors.

For example, If we apply a sheer matrix 3 times to a vector. This doesn't change the eigen vector direction but it will change the magnitude of the sheering because we apply it three times rather than one time so of course the eigen value associated with the composition of all three together must be the same magnitude change if we applied sheer as three separate transformations.

[zhewang]

The videos are SO HELPFUL! I had no idea what my professor was talking about during my lecture. Now, I actually understand stuff!!!

[sergiocontrerask]

It is impressive how to this day this knowledge has not been lost, I mean, YouTube videos are always difficult to watch after years, not this one, it is just as good today, that when it was done

[hasanshirazi]

Thanks a lot Professor. Your lecture clarified the eigenvalues and eigenvectors very well.

[davidwright]

Many thanks, Gil! If all math instruction were as clearly and carefully explained as yours, math would be a lot more popular - because people would realize it was something they could do - like riding a bicycle!

[ashishneupane]

That's why everybody wants to get into MIT. My professor needs to see your lectures.

[joefagan]

My word!!!! Every sentence is precious 💝💝