Linear Algebra 13e: The LU Decomposition

[@MathTheBeautiful]

Go to LEM.MA/LA for videos, exercises, and to ask us questions directly.

[@TMattos]

I very much doubt you'll ever read this, Professor Pavel, but in case it does happen: I hope that one day I'll get to contribute to society by teaching as thoughtfully and diligently as you do. Many a time I see colleagues, as I do myself, feeling stupid and becoming insecure or even developing anxiety and depression simply because most professors don't impart knowledge but rather mere procedures to solve exercises. Much respect, from a brazilian fan. :)

[@MathTheBeautiful]

Hey Thomas, I read all comments and I particularly appreciate comments like this. Thank you for it! Pavel

[@TMattos]

Made my day! :)

[@treehuggerabby123]

Prof. Pavel, Thank you so much for this video. I'm an aspiring mathematician and studying to become a math teacher. I am currently a peer educator for Chaffey College in California and I work at a local tutoring place. My goal is to become a math professor! However, I have several learning disabilities that make it hard for me to understand textbooks. It's been a while since I've heard a mathematical concept explained so succintly and clearly. It brought me such joy to be able to understand this concept and be able to explain it to someone else. Upon watching this video, I pulled my husband aside to watch this video in sheer excitement! It was so easy to understand for him, as well! Thank you for bringing a smile and knowledge to me. I can't wait to use the techniques here! I hope I can leave even a portion of the impact you leave on the world every day on my current and future students! Sincerely, A.M. Vega

[@MathTheBeautiful]

Hi A.M. Vega, Thank you for such kind words - it made my day! Good luck in your admirable endeavors! Pavel

[@sophiazhang7556]

It is fascinating to see how a video from 2014 help in 2020! Thank you so much! We really appreciate your work!

[@MathTheBeautiful]

Thank you, Sophia. (Expecting the same impact in 2120, though.)

[@dannuttle9005]

I was reading about LU decomposition in a book and it was the usual abstract material I can't absorb. This video made it crystal clear and simple.

[@ektabansal5332]

I am learning linear algebra first time and I found you professor, thanks for this whole playlist

[@antonellomascarello4698]

This linear algebra course is a joy to watch... I wish I had a professor like you when I studied this subject for the first time ... I'm starting to love linear algebra 😀 thank you 🙂🙏

[@justinoboyle5767]

Thanks so much for this. This has added much-needed clarity to this topic for me.

[@xicosim6524]

Thank you very much. Your videos are the best on this subject, by far.

[@balakumaravel7034]

wow! i had previously watched a video on LU decomposition but they only gave the process and not the explanation. dissatisfied i had come to your channel.now i think i understand it well.thank you sir

[@MathTheBeautiful]

Thank you for your comment - it's deeply appreciated!

[@brentlocher5049]

This is my first video that I tuned into on your series to gather further insight into A=LU. This is really good. I love your side commentary that adds perspective. I will be watching your videos to understand linear algebra going forward (BTW 3blue1brown has greatly helped me get my linear algebra "thinking hat" on, but I need to now fill in the details.).

[@Jr-jx4yv]

This was a great way to explain LU decomposition. Thank you very much

[@MathTheBeautiful]

Thank you for your kind works - it's much appreciated!

[@garrenmiller6737]

Wow. This was very helpful. Much better than most of the other stuff even available. Thanks.

[@sandrasandeep9332]

Thank you - a million times over!

[@Gojam12]

That is a fantastic explanation.

[@MathTheBeautiful]

Glad you liked it!

[@MikeHawk-s2g]

This was an excellent explanation!!! Thank you so much!

[@julienmciver6454]

You really are a great math teacher.

[@MathTheBeautiful]

Thank you, that means a lot!

[@gunyolk55]

This is very beautiful!

[@hotspringroll]

thank you! your clear explanation made the lesson very easy to follow!

[@sangwoopark7027]

I don't see how [1 0 0 ; -4 1 0 ; -7 0 1] is an elementary matrix. Isn't an elementary matrix one that which can be obtained by a single elementary row operation on the identity matrix? I think the matrix above requires two operations (even though it can be applied at the same time).

[@MathTheBeautiful]

+SangWoo Park We define an elementary matrix as one that's a handful of easy-to-see operations away from the identity..

[@egeoncel6379]

How about PA=LU? Can you help with that as well?

[@homayounyaqobi792]

Your work is a great man. Thanks so much.

[@Deliverance34]

Thank you, very helpful. Also you have beautiful handwriting!

[@guccilover2009]

Thank you for such a good lecture on LU!

[@ParthKohli]

We can save some steps by noticing that the inverse of an elementary matrix is the elementary matrix of the inverse operation.

[@FarisMQ]

thank you , you are so great in doing this

[@holyshit922]

If I have to write a program for LU decomposition I wouldn't use product of inverses to get matrix L Each iteration of gaussian elimination gives us zeroes in the column below diagonal so we can insert there multipliers used for elimination and skip this and previous columns in elimination I would introduce an auxiliary vector to record row interchanges

[@skyvcx]

what a great explanation. thank you very much for this video.

[@seanlane812]

Wow that was an amazing explanation. Thank you!

[@nila-333]

Thank you so much.

[@natalies1592]

Thank you!! This was very helpful

[@chocodil2]

How does switching the location of pivot on the matrix (ie switching rows) improve numerical stability? In this example how would we switch the rows of A without performing the first step of GJ elimination?

[@MathTheBeautiful]

I didn't explain this in the video, but I think that you will find an example of things going wrong numerically in the following link: math.stackexchange.com/questions/1143471/gauss-jordan-elimation-unstable

[@victorserras]

This is fantastic, thanks

[@1997tennis]

Excellent!!! Thank you!

[@ashishgor2163]

Thank you sir 🙏

[@Economy456]

Excellent video!

[@moniquetaho106]

Thank you

[@isaacenyogoi9004]

Thank you.

[@footage6402]

does L1 times A equal that matrix result?

[@therabbit3307]

Thank hou!!

[@alexandrostsagkaropoulos]

Perfect!

[@لعبهالقدر-ج7ه]

my graduation research title is( LU factorization)..can you help me?

[@MathTheBeautiful]

Sure!

[@لعبهالقدر-ج7ه]

Lemma Can you help me find sources I can benefit from?

[@لعبهالقدر-ج7ه]

Lemma what's your facebook account?

[@49adit]

Is that David Wallace

[@holyshit922]

The way he presented it is not so useful for writing a program in languages like Pascal or C Even for pencil and paper calculation it is easier and quicker to do gaussian elimination with record of multipliers

[@kalyanben10]

long shot.. but still hoping to get an answer. I asked the following question on math exchange math.stackexchange.com/questions/3605451/checking-is-a-point-lies-inside-the-area-enclosed-by-multiple-equations-using-li . can you help?

[@newbie6036]

Psychologically lower triangular lol

[@emperorpingusmathchannel5365]

Thank you so fucking much

[@senzongubane7773]

this guy is amazing at what he does but hes extra some of us are just engineering students and we're concerned with the procedure but aside from that good work

[@seandafny]

Ur not an engineer

[@senzongubane7773]

yes not yet

[@senzongubane7773]

It is societies tendency of labeling and putting stereotypes , that an engineer is a particular type of person that is the human beings down fall ,don't look at my preferences and think you can sum me up with just a comment you can not begin to fathom the depths of me.

[@oleksandrkhomandyak3860]

even in the 2024 you teach to a nobody that want to become somebody how to understand things

[@mastrammeena328]

Awesome Schaums outline linear algebra didn't have it's proof

[@MathTheBeautiful]

Glad you liked it!

[@holyshit922]

This way of teaching LU decomposition is useless for programmers

[@ts-ny6mx]

Thank you very much! This was really helpful!

[@MathTheBeautiful]

Thank you. Glad it helped! Check out lem.ma/LA while you're at it!

[@yaling1865]

Thank you!

[@humayun7062]

Thank you