I love MIT Open Courseware. They always allow me to understand theorems faster!!

dude you were great...thanks a million

DUDE! I Had this instructor! HE IS AMAZING!

This video literally solves the problem that has haunted me for weeks. He is my life saver.

Professor Ben Harris, thank you for an excellent video/lecture on LU Decomposition in Linear Algebra. This is an error free video/lecture on KZread.

Very well explained. Thank you very much!

This was amazingly helpful, thank you very much. Congratulations on keeping such meticulous records of your steps.

Well done presentation/explanation of LU Decomposition. Thank you for that Ben. :)

better than my teacher even i dont speak english lol

@freddoran1665

4 жыл бұрын

İtüden geldik biz de buraya :( Mat281'in ABV

@kdoodoo

4 жыл бұрын

better than my teacher even he speaks english lol

Thank you Ben

Great explanation. Thank you, man!

Yup, 10 minutes solved my week-long agony.

much appreciation! thanks Ben

I finally understood this!

Thanks for sharing. Wonderful explanation!!

Thank you verry much Ben :D , I ve learned so much!!!

Very clear and concise. Thanks for the example

Very comprehensive. Thank you.

Very nice explanation, Ben, Understood each and everything of it. Thank you very much.

Learnt the method quicker than in 2 hours at my numerical methods class. Superb.

Thanx to you now I know LU factorization. Thank you sir. you are doing a great job.

Great explanation, thanks!

Excellent!!! Thank you very much

AMAZING

Awesome video!

Yes! Thanks for your comment at end of the video! I was requiring that U was not singular, but it's not necessary for LU decomposition. =) So... if you want to ensure that the LU decomposition exists you just need all submatrixs be nonsingular except the matrix you are trying to decompose in LU.

your a life saver ben

the elementary matrix needed for permutation is not lower triangular so it's not useful for getting our L matrix since it would defeat the purpose. The best you can do is getting an extra permutation matrix known as P to get PA=LU but you can't be guaranteed to get A=LU by exchanging rows.

Thank you so much

Thanks a lot. It really helped me

good work done Ben keep it up

this is very helpful!

Thanks a lot.

VERY CLEAR, THANKS

Cool and clear.

thanks a million dude

Thanks a lot!

So clear ;A; Thanks!

Thank you sooo much sir

very helpful. thank you

Thanks!

thank you :)

Nice Job!!

nice explanation thanks 👍👍

Just missed one point here: the decomposition will exists if a=0 and b=0 at the same time.

@obi-wankenobi9871

5 жыл бұрын

In tasks like that one, you usually have a restriced domain, so you arent allowed to simply use zero.

Good One.. thumbs up MIT.... (Y)

You'll need to use the permutation matrix known as P, so PA = LU. Google it, cheers.

helpfull thanks.

*Good.*

Why lu decomposition doesn’t work if we have to do row exchanges?

@drdale104

4 жыл бұрын

It can work, but then you have to multiply by a pivot matrix on both sides. To make things easier, if I'm in the middle of a problem and I notice I need to make a pivot I will restart the question and have my first step being multiplying by a pivot matrix. But you can usually tell right off the bat if you need to pivot. But for this problem, since it was working with variables, an assumption had to be made.

Damn, the dude solved it like a magic trick.

does this work if we put the ones in the U matrix instead of L

#Excelent!

Cool.

Very helpful! Question: Why does LU Decomposition only work when not doing row exchanges to get U (9:15)?

@Belandbec

10 жыл бұрын

Because you are "registering" your operations in the L matrix. So if you change the order of the rows or columns, you may screw up with the L matrix elements position. That's my guess

Ben.....you're doing a great job but you guys should always pay homage to Gilbert Strang as well.....Thanks for your most excellent factorization.

Great :D

Thanks redpussy to make me understand how to read permutation matrix :D cause Gulina only could talk about donuts

Okay... Thanks... :'D

can I kindly get a reference material on this topic

"Okey! Thanks."

@kabirbaghel8835

4 жыл бұрын

thenks

A little question: What if a and b both equal zero? I think in this case, the matrix has its LU-decomposition too.

@coal2710

7 жыл бұрын

No.We are assuming these matrices are elementary.And as a rule,if a row is full of zeros,that row should be the last row of matrix.

Yellow head knows something.

I dont get how he worked out the elimination matrix? at 2:35 can someone help please.

@ElektrikAkar

8 жыл бұрын

+Sahamat Haque Think about rows. Look at the indices of elements in E matrix. E matrix is like; e11 e12 e13 e21 e22 e23 e31 e32 e33 and an arbitrary element is eij isn't it? Here i corresponds NEW matrix's row and the j is old matrix's row. Let me explain; e11 = 1st row of NEW matrix includes 1st row of old matrix how many times? Of course 1 time. Because they are idendical. Old 1st row * 1 = New 1st row. e12 = 1st row of NEW matrix includes 2nd row of old matrix how many times? ZERO. e13 = also zero. But for the elimination pusposes what he did is that he added first row of old matrix to second row. To eliminate something. How many times? a times. So new 2nd row is = OLD's second row + a times OLD's first row. e21 = 2nd row of NEW includes how many of 1st row of OLD = a ; e22 = 2nd row of NEW includes one times of 2nd row of OLD = 1; e23 = we did not do anything about 3rd row so is 0. It is like that.

@sahamathaque5088

8 жыл бұрын

thank you very much! This was very helpful :D

I know, but that's because you have only watched this video. You can watch the whole course provided free by MIT to understand it.

in the U matrix if a=b the matrix U is singolar (det=o). a not ugual b is another condition for the U existence?

@MrRenanwill

6 жыл бұрын

No... U read the definition of U and you will see that U dont need to be nonsingular (... it's just a Upper triangular matrix. =)

Which university? Not MIT of course, this is just a 9min video, MIT has uploaded entire courses of linear algebra that you can take and understand these procedures.

"good"

@batfishh

6 жыл бұрын

you're god damn right

@obi-wankenobi9871

5 жыл бұрын

I now understand why people are impressed, when you say you were at the MIT. The explaination is garbage.

Can someone explain me in more details the last thing he says. Why a-b (even though is a pivot) can be zero?

@jogaserbia

9 жыл бұрын

Salvatore Cipolla "a" is the pivot, not "a-b". at 3:56

@fugisawa

8 жыл бұрын

+jogaserbia +Salvatore Cipolla But a-b is also a pivot. It is the pivot of the third row, after the elimination. I believe (a - b) ≠ 0 is also a condition.

@SilverArro

8 жыл бұрын

+Daniel Fugisawa He explains this exactly at the end of the video. Row 3 does not need to have a pivot in order for A to successfully factor into LU. If the third column of A has no pivot, then it simply we means we have a singular, rank 2 matrix, and as Ben explains, singular matrices can still have LU decompositions. The important thing is to avoid row permutations, and since row 3 is the last row, there's no need to exchange it with another in order to transform A into U. From Wikipedia: "If A is a singular matrix of rank k, then it admits an LU factorization if the first k-leading principal minors are nonsingular." In the case where a=b, the matrix has rank 2 and the first 2 principal minors are 1 and a. Both of those are non-zero, and thus the LU decomposition still holds. Therefore, a - b CAN be zero.

@mrngkahwee95

7 жыл бұрын

Hi, I may be wrong, But, for upper triangular matrix, we are only concerned with entries below the diagonal ones to be zero. A Zero matrix (all zero elements-including diagonal) is still considered to be of a upper triangular form.

why couldn't we do row exchange in the elimination part in LU decomposition? I remember my professor taught about partial pivoting in Gauss Elimination and LU decomposition.

what is L and what is U? why is it called that

Suppose b=0. Then a0 is OK. So a0 alone is too restrictive.

@jimmonte9826

4 жыл бұрын

Sorry -- Meant to write that if b = 0, then a = 0 is allowed. L is the identity matrix and u11 = u13 = 1 and other uij are 0.

That is why its called MIT lol

seriously? you're watching a homework solution without knowing the theory? the complete lectures where the whole theory is developed and easy to understand is uploaded on MIT's channel. You can't just expect a whole lecture done from scratch for every homework solution posted.

Young Gilbert Strang haha

what does it mean "LU"?! :)

@julianabucher

10 жыл бұрын

L: lower triangular matrix. U: upper triangular matrix. This method factors A into two matrices, L * U.

@RomiiLeeh

10 жыл бұрын

Thank you so much! :)

you study this in MIT ? it's exactly like in our college :o I should study there :o

when you hear MIT, you expect some higher lvl things, but it turned out just like a normal college :/

daddy

weak ending

T U R K E y

Hindi jante ho toh Bhagwan SIngh Vishwakarma ke channel se par lo.Faru samjhate hain.Ye firangi theek se para nahi pa raha hain

what a bad explanation blet, worse than even İbiş

@kabirbaghel8835

4 жыл бұрын

wat