Lec 21 | MIT 18.06 Linear Algebra, Spring 2005

[AntoMelta]

Good, I like that you share this video, I wish success always Eigenvalues and Eigenvectors.

[willamricard]

Nice Video Eigenvalues and Eigenvectors That You Share , So Very Nice Thanks You

[imegatrone]

I Really Like The Video Eigenvalues and Eigenvectors From Your

[bundawartini]

Your Video Eigenvalues and Eigenvectors Is Very Useful Sharing

[Imbacordes]

Oh this is really saving my course

[noorceen]

he is amazing :)

[RegineCarened186]

na wer is deutsch

[59thbridge]

Man. I hope those students realize what an amazing teacher they have. Teachers that great are slim pickin's.

[Wingedzephir]

Great! I think this is one of the best linear algebra lectures I have ever seen!

[Labyrinthofmysoul]

Savior for me.

[jpmartineau]

Holy shit this is so much clearer than what I learned in college.

[haldur86]

@jpmartineau This is so much clearer than what Im learning right now at my college :)

[dinodonia]

I'm taking this course at another popular university right now and it's nice to see a professor explaining this in clear english.

[bje717i]

@dinodonia

what university? I am taking this course right now too at a popular university.

[enkii82]

@bje717i MIT

[salgadoxilinx]

this guy is a fucking teaching genius, period.

[suvrakantichakrabort]

awesome



[akhil089]

thanks professor gilbert

[TSUKItsuki19]

i love your lectures Mr.Strang!

you give a completely practical and intuitive meaning to mathematics concepts!

Thank you!

[hypnoticpoisons]

boooooooo *thumb up*

[LAnonHubbard]

Enjoyed this lecture. Even laughed out loud in a couple of places.

[eddsaunders1]

λ is an eigenvalue if dim(Vλ) > 0, i.e., if ker(T − λI) is not equal to {0}, which means that (T − λI) is not invertible, and so det(T − λI) = 0.

[MatrixOfDynamism]

WHY MUST A-yI BE SINGULAR??

[hypnoticpoisons]

@MatrixOfDynamism

you wanna find the eigenvector x (apart from the zerovector) with the property Ax=λx => (A-λI)x=0

so if there is an nonzero solution x, (A-λI) must not be invertible, in other words the term must be singular.

[amazingx87]

otherwise there will be a minus in front of the lumda and negative signs will cause subsequent steps to be tedious and probably cause some careless mistakes lol

[amazingx87]

WRONG eqn at the beginning. To find eigenvalues, set det( lumda I - A)=0 and not det (A- lumda I) as he wrote on the board. other than that great lecture

[alang504]

@amazingx87 you can do it either way,

[alang504]

@amazingx87 you can do it either way.

[blackrobe2007]

ugg I hate it when the audio is not right..great lecture tho

[robyniscool99]

life saver before my final exam tomorrow,I know everything else perfectly except eigenvectors, thanks a lot MIT

[gachmari]

not perfect but he figures out some cool features ...

[dragovian]

thanks for this brilliant explanation. Yet I wonder why lambda_1 and lambda_2 don't add up to 0 for the second example, A=[3 1; 1 3]

[dragovian]

@dragovian whoops, my mistake. They add up to 6, which are the diagonal numbers of A. Looking at the wrong matrix

[benzbubblecat]

lol I want to meet the 3 people who "disliked" this...who "dislikes" a linear algebra lecture....

[DarcyWLincoln]

Thanks the Internet! I'm now a MIT student!

[sdcororaton]

Brilliant, brilliant lecture! All books I have read go straight to the algebra of computing the eigenvalues and eigenvectors without explaining the underlying meaning and make it so complicated. The simplicity of his explanation is pure brilliance!

[yoyaya007]

lucky you MIT students !!!!

[muaythad]

Thanks Strang, this explanation is awesome. I think that all Linear Algebra courses must indicate those videos as a kind of homework.

[twirmd]

I have an absolutely awful professor for Linear Algebra. These video lectures are the only reason why I am getting an A in the class.

[paulnscheidt]

This is the best explanation of Eigenvectors I have yet heard! 6 Stars!

[phdivancrace]

It is amazing, I love to watch this videos. Thanks Gilbert Strang and MIT.

[padmanandm]

He should be awarded Nobel prize for education.

[athoverlord]

If I had had such teachers... Just brilliant! Thank you very much prof. Strang!

[berkeley73]

Have a good weekend.

A real New England weekend.

[musa78692]

'innocent looking quadratic' :D

[juhxmn2]

Amazing lectures, Strang always helps! Thank you very very much!

[dougotgame33]

I use this guy to teach me what my teacher was terrible at teaching. He's a lifesaver.

[powerfury]

Strang is probably the best lecturer I have seen on linear algebra.

[ezhavapanicker]

the guy is genius..

[DaWanderer]

dude this is why i love the internet

share the knowledge!!!!

dr. strang is the man!

[iwalkedonthesun]

Prof. Strang, I love you! An honest THANK YOU!

Thanks to you I had 18 in linear Algebra :D

[aesklava]

Thanks for putting this on youtube! This really helped me!

[fza421]

Really good lecture,better than my professor in uni

[russelljbarry15]

This lecture is so important to quantum mechanics, that it is a good review for the linear algebra behind it. I also give it six stars (so what it can only have 5).

Great lecture

[akska8]

Is there a way to give this 6 stars?

Really, premium stuff.

[anbarasan109]

hearty thanks for sharing

[AbreValas]

Awesome lesson