Lec 4 | MIT 18.06 Linear Algebra, Spring 2005

[TheJacChannel]

why am i watching this

[jorginho1726]

does anyone know the name of that algebra text?... or where can i find it?

[sivrisinekk]

Good but I think it recorded by dean's mobile phone

[NganaJHone]

I am very happy to see the vidoe after you give this Factorization into A = LU

[Ondelendo]

Steady I Really Like This Video Factorization into A = LU

[bebeheuy]

Good, I like that you share this video Lecture 4: Factorization into A = LU, I wish success always

[willamricard]

Nice Video That You Share , So Very Nice Thanks You Factorization into A = LU

[imegatrone]

I Really Like The Video Factorization into A = LU From Your

[bundawartini]

Your Video Factorization into A = LU Is Very Useful Sharing

[anakmudajaman]

after i watched this video Factorization into A = LU, my insight is very open because the video is very good to give information

[WhitEagle7]

240p? are you serious?

[QuantumMadcow]

Thanks to MIT open courseware I was able to get my entire freshman and sophomore math curricula out of the way for pennies on the dollar by using credit by exam... not to mention skipping ahead in my major (physics) by a full year. Thanks, MIT!

[TheMingusjazz]

Das Bild ist nicht gut, ist die Klasse Englisch, aber es ist eine gute Lektion.

[akhil089]

thanks professor strang



[SirZagga]

Thank you MIT for embracing the true purpose of science and publishing these lectures!

[bucky765]

I took linear algebra years ago in college, but I thought I'd brush up on it in preparation for the Stanford AI free class in Oct 2011 (it's being taught by a director at Google). I've been working heavily in ado.net for the past couple of years, and it's surprising just how how applicable this is to the work I've been doing. Anyway, I'm thankful MIT decided to put these lectures online.

[trese0000]

I hope that there are NO MORE video lectures in the series that are this low quality in sound and picture.

[ricsurfpro]

I realy need that lecture and, but image and sound hav bad quality !!

[andywuu2002]

The video quality is absolutely not tolerable!

[jdunn015]

Not sure if I understand the cost approximation. I interpret it as: if row 1 of 99 entries multiplies row 2 of 99 entries in order to get the pivot entry 2,1 then this operation is equal to 99 multiplications. So in the end when he is estimating the cost of just column b then wouldn't the cost be 100+99+98...+1 instead of n^2.

[GoPila1989]

is it right that he called a operation (subtraction and multipliaction)? Okay then 100 square operation is right. in other case, we have ~100^2 multiplication AND subtractions. thats 2*100^2?

[xgokkusagix]

where did he find -4 in the E(21) its not clear and also there is tooooo much noise.

[SpoiledLogic]

If you are having trouble viewing this lecture, open up the interactive transcript...it helps.

[adidasguy87]

Im not very got at linear algebra..which is why i watch these videos.. can someone explain to me how the first number for the approximation is 100^2. I understand he is counting the maximum number of multiplications and subtractions but i guessed the first number was 99^2 because i thought you always leave the first row unchanged

[feng264404]

@adidasguy87 yeah but if you consider the special case where first pivot is 0, you would need 100^2 operations

[BlackMage1016]

@adidasguy87 Notice that he said "about" 100^2 for the first set of operations. The actual number of operation is 100*99, and when dealing with complexity you always round up. Estimation of complexity is more about getting a general picture rather than seeing how exact you can be.

[waqar0204]

great job ... thanks

[mohinder3333]

its shot in 2005Why does it look like its from the 80s..lol

[spectralblue]

@mohinder3333 Actually it was shot it 1999. That explains why.

[raneboy13]

they're MIT and cant afford SUPER DUPER HD video recorders?

[spectralblue]

@raneboy13 HD recorders were very expensive and bulky and only used by the movie industry at the time of this video (1999).

[raneboy13]

@spectralblue mr. g strang cant buy hd recorders?

[spectralblue]

@raneboy13 He can of course, but at the time at this video again, back in 1999, there was no need for HD except by the movie industry, who had to project an image in a big screen. In fact, a majority of TV's and computer monitors can't even display HD. So there was no need back then. And they were probably happy with the quality of this video back then. Get it?

[92sanxez]

This is so nice. Free education, wow, i can't even believe it.

Thanks to the people who made this possible, they are great.

[ikanipo]

I can't believe people are complaining over a free lecture. Either go buy a book and learn it yourself, or be quiet. can't complain when they are offering it for free. I think these videos are awesome, all things considered. if you have trouble reading the numbers....pause the video when they zoom in. Problem solved.

[leegoldberg]

@ikanipo +1

[32docholiday]

the high definition on this video is amazing....

[AleifrLeifrson]

This looks like it's a rip of a rip og a rip that was taken with a 1 megapixel phone...why is their quality so bad so often?!

[thyorison]

This was recorded in early Spring, 2005. On the morning of January 14 (a Friday) of that year, the Huygens probe landed on Titan. That might explain, but not excuse, the rudeness of the MIT students in this lecture.

Don't be discouraged by this lecture. The rest of the series is excellent.

- Ray Eston Smith Jr

[iyalovecky]

great explanation but very low quality((

[RingWarrior12]

i bet he confused a lot of students with his explanation of A =LU

[klavierfan]

no HD makes this lecture hard to view...

[trecedelemos]

Why is a MIT professor teaching high school math in an undergrad course? 2+2 = ?

[KSH2006]

@trecedelemos

It is linear algebra...

[xploi]

If the subtitles were synchronized tese lectures would be just perfect

[gontrodestraat]

I don't understand why when he counts the total number of operations needed to tranform matrix A, namely the same of 1^2+2^2+...+n^2, he uses caculus method to approximate the total number, while we know that the discrete sum of squared natural numbers is equal to n*(n+1)*(n+2)/6....

[Diemedes]

@gontrodestraat

If you read his book about Linear Algebra, you'll see why he is so interested in approximating the number operations needed to either solve a system, find a determinant, etc.

Basically it's because if you have a huge number of equations, you have to use a computer. But the technique you are going to use in order to perform your desired operation is based upon the number of operations needed. Less operations=faster computation.

[Kyrgyzstudent]

Thank You very much for these useful free courses!

[earthday1988]

What happened to the video quality . Isn't a good version available . I mean it is sometimes hard to see what the professor is writing on the board.

[LutherSetzer]

This video helped me to break through some mental blocks in understanding the concept of LU decomposition and how to construct elementary matrices. Thank you, MIT, for making this material available at no cost to viewers. Gilbert Strang R-O-C-K-S!

[thou9009]

Why is everyone complaining? Free lectures? This is only one vid out of many. It's not that bad once the students are quiet. Love G. Strang.

[trousien]

wow what happened to this lecture its so bad quality and not only hard to see what he writes but hard to listen with the noise and everything... its still beats reading the book and my professors lecture but not what i'd expect from the qualities of all the other lectures i got from Linear Algebra from MIT

[eyeojo]

Wahh, this free resource isn't what I paid for, wahh

[Chubigans]

Okay so i'm reading the textbook for this one.. can't watch this lecture without crying

[nandinis7]

the sub-titles are not exactly in sync with the video :(

[rehxyz]

Ah, what Professor Strang offers on how many operations it'll take is a little strange. the n^2 and n^3 are very poor estimates. You could just imagine removing a triangle from the matrix, the area of that triangle would give the required operations at maximum. Or n(m-1)/2 = max ops. Since we're removing a triangle of dimensions (m-1) (since we do not touch the first row), times n. For a m by n matrix.

Later,

rEhxyz

[gontrodestraat]

@rehxyz I agree with you, this n^2 approximation is quite poor. First, we don't know what will be the results after our operations. second, I guess he takes the max max operations.

[Yizashi]

@rehxyz , I'd tend to agree, except to point out that we're talking about an n x n matrix, so n(n-1)/2. Of course, I assume he knows something we don't, because he's lecturing at MIT and I'm watching videos on youtube 0_o

[nevertalk]

I loved the sock/shoe analogy!!! Math nerds ftw hehe :D!

[duraduri]

i'm so sad, because there is no HD

[rammps1982]

Why is so much noise in the class during the lecture?

[metacarpi]

@rammps1982

It's probably aliasing from the high compression of the sound. There's no higher quality version available anywhere.

[fullmooninu]

@rammps1982 it aint germany

[rryking]

@rammps1982 prob another ivy slacker pass/fail class

[Xenxe777]

LOL @ comments from meet the spy

[chaohord]

I didn't see Gordon Freeman in the crowd.

Unless, he was a SPY.

[tacxof]

very easy...simple equation

[w1ngzer0]

the thing i like about the MIT videos is the fact they include subtitles because sometimes you cannot quite understand what they are saying sometimes.

The video quality looks like it was recorded with a backup camera. =P

[seisdoesmatter]

linear algebra is easy

[woserzing]

mit rocks

[kyousukeX]

I got "A" this course. i think it was the most fun math course.^^;

[yoinkity]

go look at uc berkeley's webcasts! much better quality!

[omhat]

man thats an abundant class sarcastically speaking for a linear algebra class at a university.

[xy9izzy]

The compression on this video is too much. The letters on the chalkboard keep wiggling and dancing around. when the camera guy pulls back, it is completely illegible.

[AgileSooftware]

わかりやすい線形代数の講義だと思う。

勉強会のねたに使えそうだ。

[JackMRich]

This is the first time ive learned Matricies ... Why would you want to transpose a matrix what benefits swapping the columns for row etc?

[heocon19ca]

One of the reason is that after studying and proving results for row space of a matrix A, you can then easily generalise them for column space of A by looking at the row space of A^T.

[EnderMB]

So far I am very impressed with the quality of these lectures. I attend a post-polytechnic university in the United Kingdom and my CS course offers very few Maths subjects, so these lecture videos are brilliant for someone looking to learn.

[jonahansen]

Hey folks, this is the guy to learn it from, too!

[ljusorange]

Much appreciated. I've missed a few lectures due to serious illnesses, and although I live in Sweden, this contribution from MIT make it possible to catch-up almost friction-free. Thanks.

[214899]

great refresh for a MA candidate, who missed a lot in BA.

[lyml]

Theese are great. I missed a large part of the education during linear algebra and with theese videos I don't have to wait untill next year to catch up but can do it as I have time.

Watching theese 35 videos is something you could do in a couple of days if you work fulltime with it.

Also, you could do it whenever you want to :).