Introduction to eigenvalues and eigenvectors | Linear Algebra | Khan Academy

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What eigenvectors and eigenvalues are and why they are interesting
Watch the next lesson: www.khanacademy.org/math/linear-algebra/alternate_bases/eigen_everything/v/linear-algebra-proof-of-formula-for-determining-eigenvalues?YT&Desc&LinearAlgebra
Missed the previous lesson?
www.khanacademy.org/math/linear-algebra/alternate_bases/orthonormal_basis/v/linear-algebra-gram-schmidt-example-with-3-basis-vectors?YT&Desc&LinearAlgebra
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.
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[@joerich9636]

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

[@razoredge8284]

shut up boomer

[@AS-nx9fu]

@@razoredge8284 😂😂😂😭😭😭

[@josuequintero-td5gh]

I can't imagine school without the internet

[@francoisbe92]

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).

[@monroe444444]

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.

[@jnv1971]

You must be searching manually on khanacademy then, which is a pretty terrible idea. If I were you, I'd just log in to khanacademy and write the name of this video into the big searchbox at the top of the page.

[@utsawin09]

has this guy been on the front cover of time magazine?? he fuckin should be.

[@dauntSilver]

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

[@moonman239]

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

[@akj375]

If I may be so bold as to suggest... could you please number the videos in each category or subject heading? That way if one doesn't catch some of the concepts in the current video, he can always go back successively until he gets to a point where he's comfortable and can again start moving forward. Much much appreciated. Thank you for everything that you do!

[@SpeaksYourWord]

Yes that would be helpful

[@guilbas1]

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

[@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

[@MarineFocus]

My prof said something about that, and no it does not make a difference except for negative signs. But since you're going to compute det(A - lambda * i) = 0 a lot of the time, the negative signs won't matter because the right hand side is 0 anyways

[@TheFarrukhnaveed]

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

[@SergiuMunteanu]

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

[@vivekkumar-py6kp]

Which previous video are you talking about??please help me

[@MisterLiBRiUMz]

I really appreciate the videos. I've got my Linear Algebra exam Monday for my first year Engineering, (Will be specifying in Chemical Engineering 2nd Year) and I can stress by saying thanks for uploading these awesome videos.

[@monamahmod8976]

I guess you are a graduate now if so good luck

[@MightyGoldenBoy]

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

[@TheYipedo]

There's a reason why he's requesting it while still being grateful and not demanding it like he's entitled to it. The purpose of this video is to help other people learn linear algebra. It's just a mere suggestion that will help people cruise through the vids swimmingly without potentially skipping crucial lessons along the way.

[@vishalvisd4]

Dear sir, you are really a big help...thanx...

[@arsenalwak]

So what is the definition of an eigenvector and eigenvalue, something i could write in an exam please.

[@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?

[@SpiritVector]

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

[@譚文雪]

I ❤ u,u r my real professor,my tuition fee should give u ,really!

[@macerik628]

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

[@abhishekravindra4008]

Best expalanation of eigenvalues and eigenvectors upto date

[@TheAncientScholar]

@imamnalog: One important, practical meaning is that Eigenvalues in the time independent form of the wave equation represent the binding energies of an electron in a Hydrogen atom at a given value called "n." This is in fact where we get the quantum numbers values for "n." They basically fall out of the Eigenvalue solutions.

[@Phagocytosis]

While that would be useful, you might consider watching the videos on the Khan Academy website instead -- it even has a cool scoring system that just makes it more fun and motivating if you're the right type of person for that kind of thing -- where they are all listed in categories and sub-categories and in order.

[@ivancarrillo1889]

I felt quite intimated by these vectors name not able to grasp what they were. Thanks for such a quiet simple yet powerful explanation.

[@jacobsan]

It's actually quite simpler than it sounds lol

[@barzhikevil6873]

Thanks for sharing!

[@shotcallerpat]

@Lexorinox Yeah it's pretty bad huh? Are you going to Berkeley? This helps so much.

[@nochiill376]

Can you please make a video on Diagonalisation Theorem?

[@yousuffarhan963]

Cantor's Diagnalization Theorem?

[@taviona]

Wow, that was so helpful.

[@tymothylim6550]

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!

[@omarolocabe]

Awesome....thanks..it was helpful...

[@Seakros]

Once again,many thanks for your videos you are doing a great job!

[@hotlemonadesauce2042]

Hey.. Still there?

[@aishah8398]

thank you khan academy... I wonder how one can make this horrible stuff so simple n understandable...you are one of the best math n stats teachers

[@galotalp]

please please please do a video on principle component analysis

[@nm4k4]

Thank you for this intuitive explanation!

[@ash11music]

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

[@CyberneticOrganism01]

Thanks, very helpful!

[@jkjonk]

I swear I just go to class now just to talk. Thanks Khan!!!

[@lamtartarus]

does it make a difference if its (A - lambda*i) instead of (lambda*i - A)?

[@mrannabee33]

Can you put sound on these? it's hard to read and pay attention to what you're doing at the same time

[@blackphosphor]

Khan your everywhere! awesome!

[@vb4max]

thank you

[@medetkhanaltynbek1442]

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

[@dheerajsinghal8802]

hey salman sir thank you very much for providing us such a great platform. That was the best explanation i ever heard thank u you very much.

[@wickedm348]

Sal, you got me man. Really appreciate your work.

[@Zoku012]

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?

[@imbsalstha]

many many thanks again

[@BlazeMrdr]

if you go to his site everything is ordered by subjects and is in chronological order.

[@imamnalog]

Ok . . . and what's the practical meaning of these eigenvalues in Schrodinger's equation ? ? ?

[@hongsukchun]

Finding it is your job. It's already a free video, I don't think the purpose of this video is to serve other's rights, just a helping tutorial.

[@x.m.caucase7841]

Just something I don't get. How do you deduce T(v)=lamnda*v - Av from T(x)=Ax ? Is there a difference between x and v? If not does it mean lamnda*v - Av = Av ? Is my question stupid?

[@x.m.caucase7841]

Actually, the next video answered my question! xD

[@cristic767]

X.M. Caucase , how did you identified "next video"? They're not numbered? I would like to get a list, but I don't figure it out. :( Can you help me, please? Thank you.

[@x.m.caucase7841]

Oh, it's been a while now. I think the video I was talking about is "finding eigenvalues and eigenvectors examples". I don't remember if identified a "next video".

[@sillystranger3721]

@@x.m.caucase7841 lolz

[@StarXnauti]

Didnt he draw the flipped version of V1 wrong? Or do i just understand it badly? Because its not in its span.

[@ShermanSitter]

its good to watch the whole thing, but the answer is at 4:45

[@sachinnegi2161]

Sir is eigen vector and eigen space the same thing??

[@karinerino]

did you even watch the video..

[@frozenstrawbs]

have you never heard of a playlist ma'am?

[@imamnalog]

@TheAncientScholar Thnx

[@miketh6]

if you want to know which video came first you just go to kanacademy org

[@imadElghourani]

@Lexorinox yupp

[@andymitrop]

I should be paying you 9K a year instead of my uni

[@imatwink]

@HunterDX77M If you go to his website at khanacademy {dot} org then he has them in order and there is a link to the next video at the top of each video.

[@taterichardson866]

Gah! " 'I' before 'E' except after 'C' "! Yet another word that breaks this rule! I guess we should also add "except, apparentlie, for words that sound like they're invented in Germanie".

[@graei]

Why doesn't my lazy ass lecturer at uni explain things this simply..? >.>

[@jimmy000]

hahahaha, agreed!

[@Hershbomb]

possibly the best comment on this video...

[@russellkilgour]

I can't take him seriously...he sounds too much like Sips!

[@Karoke77]

2+2=4. Am I ready???

[@DavidBrit101]

you first need to know 1 + 1 = 2

[@pmecan]

Lin Alg Joke! What do you call an eigen-sheep? - - A LAMB! DUH!

[@superjokerrr]

you talk so fast

[@jimbaker5110]

He uses a whole lot of words and sentences just to explain something very simple. It’s frustrating.

[@H1TMANactual]

Well then after you learn the subject, make your own videos in non-bastardized English.