Introduction to eigenvalues and eigenvectors | Linear Algebra | Khan Academy

What eigenvectors and eigenvalues are and why they are interesting

Missed the previous lesson?

Linear Algebra on Khan Academy: Have you ever wondered what the difference is between speed and velocity? Ever try to visualize in four dimensions or six or seven? Linear algebra describes things in two dimensions, but many of the concepts can be extended into three, four or more. Linear algebra implies two dimensional reasoning, however, the concepts covered in linear algebra provide the basis for multi-dimensional representations of mathematical reasoning. Matrices, vectors, vector spaces, transformations, eigenvectors/values all help us to visualize and understand multi dimensional concepts. This is an advanced course normally taken by science or engineering majors after taking at least two semesters of calculus (although calculus really isn't a prereq) so don't confuse this with regular high school algebra.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

[utsawin]

has this guy been on the front cover of time magazine??

he fuckin should be.

[joerich]

How I wish Khan Academy existed when I was a student in the late 60s early 70s.

[francoisbe]

The eigenvectors of a transformation are the non-zero vectors that remain parallel to the original vector after the transformation.
The eigenvalue is the scalar that gives you the vector (if you have a transformation A, a vector v and a scalar t --> Av=tv. t is the eigenvalue).

[moonman]

So, an eigenvector is simply the vector that's scaled by the multiple that is also known as the eigenvalue.

[dauntSilver]

"if this doesnt look familiar to you, i can jog your memory a little bit"... he read my freakin mind! love this guy.

[monroe]

These videos would be so much more useful if we could tell which videos preceded them, as you say to do in the video itself. I have just been searching on Khan Academy for this video and the ones you way to watch before it, but I can't even find this one.

[macerik]

Right pace, clear, no waffle. Thanks
ot: what s/ware are you using - looks very effective

[tymothylim]

Thank you very much for this video! It really helped to explain eigenvectors of transformations as those that are simply scaled by a scalar (i.e. the associated eigenvalue)! The rotation analogy of the 2D case really helps visualize it!

[mrfrankincense]

Hey, Sal, I couldn't find a lot of the linear algebra videos directly from the playlist. Have I made a mistake, or have some not been put in the playlist?

[SergiuMunteanu]

You are the best math teacher I know. Keep up the good work.

[shonhayashi]

Wow, thank you so much for putting up these videos! You teach it much better than my lin alg prof, who never once explained the geometric meaning of eigenvectors/values

[guilbas]

I'm from brazil and I have a Russian linear algebra teacher who barely speaks portuguese, THANK GOD for Khanacademy!

[MightyGoldenBoy]

Thank you!!!! just started my several variable calculus and the lecturer explained this in under five secounds :P Now i get it!

[nmk]

Thank you for this intuitive explanation!

[ashmusic]

Can anyone plz send the link to the video where he explains about the reflection about the line? Thanks!

[SpiritVector]

Thanks to this guy, I am fluent in Group theory, and Number theory.

[medetkhanaltynbek]

Could you please create video about Lie derivatives, Lyapunov function..all about nonlinear dynamical systems?

[abhishekravindra]

Best expalanation of eigenvalues and eigenvectors upto date

[TheFarrukhnaveed]

Please Plz Plz :Provide index of ur lectures...plz.... they are so good.

[Zoku]

Does an eigenvalue correspond to the slope of the spanning line? For example, the line he drew corresponding to lambda = 5 has a slope of 5 right?