Finding eigenvectors and eigenspaces example | Linear Algebra | Khan Academy

[@chrisatronx]

"For any" -Sal Khan

[@tadm123]

Sal you have seriosuly a gift of teaching. I just need to sit back and watch your videos and suddently the urge to get a book and take notes hits me because, I learned something else. With you learning is so simple. Im not gonna lie I hope you win the Nobel prize in the future, you're doing a huge favor to everyone in the world

[@Mantiskova]

Thanks man! I take ages to understand stuff, and rewinding your explanation at the end over and over again really helped a lot! The thing with live lectures for me is that if i miss a sentence I may as well go home, because I'm confused for the rest of the lecture.

[@KS622]

My hero, you know I skip class and watch these videos which are far more helpful! Your explanation is very easy to follow

[@quintillusapollon5292]

If you watch the proof video (which I highly recommend) you will see that at the beginning when Av=&v we can either write Av-&v=0(vector) OR &v-Av=0(vector). Proceeding with the rest of the proof should convince you that taking the determinant of either (A-&I) or (&I-A) will work.

[@SAVAGEturtle19]

Everyone seems they reached out to this right before a test! I'm just glad I could do my homework now :D

[@BoZhaoengineering]

This is one of best interpretation of eigen value and eigen space.

[@dmowashere]

i literally applauded for this guy after this video. Lifesaver.

[@elmariachistar]

dude i want to thank you so much, today in math class I had to do exactly what you are teaching in this video and i got 20 out of 20 :), thus passed mathclass :P! ty man!

[@fox8340]

Watch his video before lecture makes me feel smart during lesson😊

[@Alzimovich2]

Thank you so much from Italy! Now maybe I could pass this linear algebra exam!

[@stunr1887]

Thank You so much I looked at my professor like he was speaking another language when he tried to teach this subject and you made it sooo clear

[@aganzechristian5660]

So how does this dude know everything?

[@Rjsipad]

reading i guess

[@royerzurumluoglu2466]

@@Rjsipad he is a Harvard computer science and math major

[@KakashiChidori616]

Because he drinks

[@nissanskyline923]

this is the most helpful video i have ever watched...thank you! you dont know how much stress you just took off of my shoulders!

[@AnnManMS]

Simply extraordinary presentation by Mr. Khan! I think you learnt this stuff from Dr. Strang at MIT. Thank you for rendering your services for less privileged.

[@DookieBlaster]

literally the same example in my practice final. Thanks for clarifying some little things. You're a beast

[@littlebigadventures]

2:34 Theres a glitch in the matrix...

[@otabekmuminov2185]

Yeah, sometimes there is

[@chasemarangu]

Aman Khosa 2:53 - 3:10

[@TheBSpaZZ]

You can make a pigeon understand linear algebra, wonderful.

[@blackhawk089]

Thanks for posting these, I had an awesome linear algebra teacher so I never went to class, and I'm still going to make an A.

[@garhwalinauna]

Thanks a ton. I love u dude.. I didn't attend this lecture in college and tommorow I have a class test on it. Really helpful. :)

[@elmariachistar]

you are totally awesome, this video is so great! I sat for 2 hours in math lecture, no idea what the hell my prof. was talkin about. I watch your 10-15 min vids and get the thing right away... you ruLE! cheers from Austria

[@scottsanerd]

Who needs to go to lectures when you have these?

[@alfiyaali2498]

Finally I have got a good teacher 😊😊😊

[@chasemarangu]

2:53 - 3:10 really emphasizing the new "eignenspace" term, great! :)

[@emaldon7]

Thank you so much, this really helped me out. I just don't get it by looking at theorems at all, I need examples.

[@williamwright4813]

You're a life saver, Sal Khan.

[@b0ondockz]

Tomorrow is my linear algebra final. The last math class I have to take. FUCK YEAH! WOOHOO!

[@catalyst013]

very helpful, thank you! I don't understand how you can write so neatly with a mouse...props.

[@gojcevic]

Thanks very much . After many years I think a gonna get it now about eigenvectors Lennart

[@alessandroboettge1640]

The geometric explanation give powers to understand everything, I feel like I can see more one dimension. Now I have Just 6 missing.

[@doubletap85]

I really wish my professor made it this easy. I shouldn't be struggling this much with this material.

[@BigSushi801]

the CORRECT equation for eigenvalues is **det(A - lamda(I)** NOT "det(lamda(I) - A)" according to Gilbert Strang.

[@kamarinelson]

PTranPhotography it shouldn't matter lol. You can multiply both sides by -1 because the determinant must be 0 for it to be an eigenvalue.

[@ronak1711993]

nice one.... thanx for this video... it really helped out.....

[@12thando34]

wow you really are amazing. all my maths and econ i learn from you...thanks a bunch

[@PerfectionKiIIs]

is there a difference between V1= -V2 and V2= -V1? The Eigenvectors would be [1,-1] or [-1,1]. I'm guessing there's no difference as the both lie on the same vector?

[@prodgex]

if you know eigen values and the eigenvectors you can multiply the modal matrix (matrix of eigenvectors) times the spectral times the modal inverse and I am pretty sure that will give you the matrix A... like so if M^-1*A*M = AS, where AS is the spectral matrix (a diagonal matrix made of the eigenvalues), then the inverse should be true, M*AS*M^-1 =A ....

[@Mike01010011]

You are a really good teacher. Thanks so much.

[@enjoyablesounds]

Great video, You might want to mention using "parametric vector form" I noticed this because I use it frequently to determine eigenvectors and bases! Handy for diagonalization! Thanks again Khan.

[@MartenWlk]

@happsider (& means lambda) If there are no mistakes in my calculations, you have got two values for eigenvalue: & = -1 and & = -3. When substituting them into [A-&I][v] = 0 it appears that the only possibility (in both cases) for v is to be zero vector (0). Since 0 cannot be an eigenvector, I conclude that there are no eigenvectors nor eigenvalues for the matrix A you provided. If I am wrong, please, can anyone correct me?

[@MsAlice729]

Thank you so much!!!. This video is super helpful!!!

[@MartenWlk]

@zxtreme09 I am not talking about the matrix: top (1 2), bottom (4 3) provided in the video, but the matrix that happsider asked about: (-3 -4) on the top and (1 0) on the bottom.

[@lukaskuth]

whats up with the reduced row echelon form you do starting at 5:21 doesnt the result matrix have to be a identity matrix with a diagonal out of 1's ??

[@frajirek90]

Could you do a video on generalised eigenvector?

[@TheStfu1000]

when would you ever have two different vectors spanning an eigen space? how would you get this from reduced row echelon method?

[@et2426]

Thank You for this vid, would be better if i watched it BEFORE i failed my finals :/ oh wells at least i have a supp exam to pass now!!

[@michaelhixson622]

Dr. Khan there is a glitch in the matrix row 1 column 1 @5:41 sign error

[@333LetLoveRule333]

My final is in 3 weeks! Feels good though!

[@karaluvsketchup]

These videos basically saved my GPA.

[@KronikSkateboarding]

im officially less fucked for my linear algebra final tomorrow.. thanks!!

[@soonwoon]

Great video! Thanks for making it!

[@happsider]

So what if the matrix to find the eigenvectors has two different results?? I had a matrix (-3 -4) on the top and (1 0) on the bottom. The top row and the bottom row yield different values for v1 and v2 so which one do i choose?!

[@Sjarlod]

@ NJMetsHero That doesn't matter since you use the determinant. All the signs are opposite, but by multiplying negatives, you still get a positive.

[@anjali9979]

Great teacher!

[@aimanacap]

at 11:00.. if i choose to let my v1=t and v2=-t . will my eigenvector t[1 -1] and yours t[-1 1] both be correct ??

[@Auryx851]

Put that matrix into reduced row echelon form, then solve for the nullspace. C:

[@anshgupta8560]

I am really confused about Null Space. Sometimes it is a span of a vector, but sometimes it is only set of one vector. I don't know when to calculate what. When is the null space a span and when is it just one vector? And how do I differentiate when to calculate what?

[@paranormaledits9526]

Thanks a lot

[@DarkFacet]

a question: is the echelon form necessary, cause i put the Lambda = 5 respectively -1 in the A*v=lambda*v and i get the same results for this exemple but i have 2 equations instead of 1... is the raw echelon form necessary for other matrices?? perhaps its a dumb question but maths confuses me.

[@dcampos0]

you are the absolute best

[@BeePan2]

How do you find the multiplicity 2 of eigenvalue?

[@ExWizI]

in a 2x2 matrix, what is after you do (lambda I - A) = 0 you get a matrix thats with first row [ 2 0] and second row [2 0] how do you find eigenvector in that case?

[@boredudez]

I wish I had watched this before my quiz...

[@otabekmuminov2185]

Which is the correct one: det(yI-A) or det(A-yI) ?

[@Alkanator]

I love this man :D

[@armanrainy]

Thank you

[@grlCycling101]

does it matter if it is (A- lamda Ide. vector)

[@AW_Designs]

hi there, great vid, so helpful. I was wondering, I am stuck on an unusual question involving eigenvectors. It asks to 'Show that if a matrix M has an eigenvector x corresponding to the eigenvalue lambda, x is also an eigenvector of the matrix M^2, and find the corresponding eigenvalue.What is the analogous result for M^n, where n is any positive integer? I would be very grateful if someone could help me out. I'll keep trying though. :)

[@keemkeemusa]

in the book det[A-&I]=0 what is the difference?

[@amitbaroi9162]

If a transformation matrix with respect to a basis other than standard basis is given do I need to find the matrix with respect to standard basis and find the eigen values ??

[@AW_Designs]

@TooNarrowToContain thank you very much, this helped a lot :)

[@Shidoremon]

you can teach better than my teacher...

[@Unkn0wn500]

Thank you so much. Finally I can burn my book from school because the explanation is so bad. You made it clear for everyone who's not that good in this stuff.

[@TansukeLoL]

because he wrote it as t[1 -1], by setting t = -1 you get [-1 1] as your result. My wager would be yes.

[@farestabs]

@TimeIsTheMatter you came all the way to Salman Khan's video on Eigenvectors to comment on a year old post? Please do yourself a favor, and take a seat, and learn your Eigenvectors before the final.

[@annog6673]

Can i Take: N(I - rref(A)) ?

[@goddess_ofchaos]

I don't get what is meant by transformation at the end of the video... can someone explain please? what is the eigenvector transformed into and why is it transformed?

[@farestabs]

prefection

[@SirTrollsAlot1000]

You can do both.

[@NetFreak]

These comment section has people who aced this exam, graduated, did phd, now successful, married life and have kids lmao

[@JizzleWright1]

It works either way I think

[@MatthewAhavah]

lol. after watching this i can say. my professor has no idea in Linear Algebra :D

[@ikedamiler]

mine is tomorrow! xD or well later today...

[@francescogiacomelli403]

ikedamiler in 15 minutes I’ll be in your situation

[@EpicUltraKingSmizzy]

if you watch how he manipulated the Ax=Lx you'd realise they're the same thing

[@techeccentric8115]

well Khan sir how didi u get lamda =5

[@nickynicknick9223]

(lamda-1)(lamda-3)-8

[@ThePengcipal]

I UNDERSTAND EVERYTHING xD no i dont but hopefully with his videos I will soon =]

[@dravidr007]

much better than strang no offense prof

[@A08041988]

say negative instead of minus

[@almerovanrooyen4463]

you forgot the negative sign in front of the 4

[@corey333p]

Final exam in one hour.

[@farestabs]

@TimeIsTheMatter cool

[@Snaaaked]

for any... for any.... for any...

[@joseluisarmenta]

why the -4 turns to 0

[@PrinceEdwardIII]

for any, for any, for any, for any....

[@NamanKankaria]

after 14 years

[@Car1ll]

@TimeIsTheMatter My god chill out...

[@Andytk33]

all dem weedz bro.

[@favour5442]

If you can ...... please slow down while teaching so our thoughts process can catch up . This is a mathematics not English

[@Fatma-mb6ii]

LEGEEEENDDDDD

[@sergiocampero3513]

#thepokigur i'd marry you if you want :D

[@thepokigur]

Marry me!!!