LU decomposition - An Example Calculation

[@brightsideofmaths]

Download the pdf version: tbsom.de/s/ov Watch my whole linear algebra course: tbsom.de/s/la If you have a non-square matrix and need row exchanges, watch here: kzbin.info/www/bejne/e2TGdIWZmat6o6c

[@MisterAdri85]

My theacher taugh me something with elimination matrix that i still can't understand. This is 10pm, i have my exams at 8am tomorrow and you just saved me a lot of points on my grade. Thanks

[@brightsideofmaths]

Good luck tomorrow. Don't forget to cite me during the exam ;)

[@MisterAdri85]

@@brightsideofmaths haha sure will !

[@PunmasterSTP]

How did your exam end up going?

[@MisterAdri85]

@@PunmasterSTP It's been a while i can't remember, but i didn't fail that's for sure cuz i entered my third year in engineering studies

[@PunmasterSTP]

@@MisterAdri85 That's awesome! How are you liking your third year?

[@notgeo3912]

This is honestly genius and simple! All the lectures out there, at least the ones I've seen, give me the whole L11, L12.... stuff and if not that, the formulas which are too much to remember and use in the exam but this is a straight-up time saver to me as I can do row operations fluently! Thanks a ton!

[@hardy4331]

I should be giving my university fees to this guy.

[@MalamIbnMalam]

LOL I agree, it's shameful for what we have to pay for at Graduate school and Undergraduate

[@eeshaanmj8656]

Then give

[@Heisenberg8307]

Contribute him in steady...

[@jamespapakyriakopoulos6187]

watched this video before my university lecture and it helped 10x more

[@PunmasterSTP]

How have your studies been going?

[@agbandanalistowel4737]

You're a genius man. You've saved me from long processes to go through. Thumbs up

[@drioko]

the colors you use help me feel more relaxed and pay attention. good choice on the yellow and warm colors

[@brightsideofmaths]

Thank you so much 😀 Some people are annoyed by the bright colors such that I also offer dark version for all videos :)

[@taruchitgoyal3735]

This was super good. I have been struggling to understand LU decomposition and it seemed the concept must very complex. But with this tutorial, all the prejudice against the topic got crushed. Thank you for the session.

[@brightsideofmaths]

Glad you enjoyed it! :) If it helps you, you can also watch my video about the PLU decomposition and download the PDF versions! :)

[@taruchitgoyal3735]

@@brightsideofmaths Thank you. Can you also publish a tutorial on SVD-Singular Value Decomposition?

[@brightsideofmaths]

@@taruchitgoyal3735 Yes, this will be part of my linear algebra series: tbsom.de/s/la

[@MalamIbnMalam]

This is a FANTASTIC explanation! I must say it is quite a bit better than what I was taught by the University of Texas in Austin. Thank you for this video!

[@PunmasterSTP]

I'm just curious; who was your professor there?

[@MalamIbnMalam]

@@PunmasterSTP Dr.Robert van de Geijn

[@PunmasterSTP]

@@MalamIbnMalam I don't want to give too many details away, but I'll just say that I was affiliated with UT Austin at some point. I never ran into that person as far as I remember. Aside from that class, how have your studies been going?

[@moon_dragon22]

I am at the end of my master studies and re-learning things for math that I need to prove for my thesis. Your videos have given me hope that I can actually do it. Sincere thanks!!!

[@brightsideofmaths]

Thank you very much and thanks for the support :)

[@Dkdkxncnchz]

u literally saved my life thank you so much

[@PunmasterSTP]

LU decomposition? More like "You are a man on a mission"...to spread knowledge and wisdom. Thanks again so much for making these videos!

[@esi5743]

Great explanation! I very much appreciate your work.

[@brightsideofmaths]

Glad you enjoyed it! And thanks for the support!

[@Virglsgames]

Wow! I am from Ukraine, so I practically did not understand anything from the words - I perceived it visually. However, I kind of got it! Thank you author!

[@zunkitgetu8042]

well u write a perfect English but u didn't understand his words?

[@Virglsgames]

@@zunkitgetu8042Yes! Is it strange?

[@vladimirsviridov3329]

@@Virglsgames yes! ahaha

[@timotheesamazingchannel3721]

This was so helpful thank you so much the first three minutes did more for me than the hour of lecture we spent on it

[@brightsideofmaths]

You're very welcome! :)

[@kkkorobbb]

Thank you so much! Exam is tomorrow, and you just opened my eyes! It's amazing!

[@brightsideofmaths]

Nice :)

[@vfrostbane225]

This was super easy to understand and explained so simply! Thank you so much!

[@brightsideofmaths]

Glad it was helpful!

[@kaif7312]

LOL, while my professor for graduate level algorithm course spent entire 2 1-hour lectures on explaining this.

[@vychuck]

Actually, your professor had to explain the foundation ogfGauss elimination to get LU done, i.e why you readily get this example.

[@justakizuner6359]

This video is just what I need! Thank you professor!

[@vychuck]

Done it really clear and accessible way

[@desmondtayes1812]

i finally found what i have been searching for amoung 10 videos. thanks

[@brightsideofmaths]

Glad I could help :)

[@RobertMurphy-wm3ge]

Excellent explanation. Thank you very much

[@ne0fuze620]

Thank you very much! This explained a lot

[@SalmanShah-w1x]

It's amazing, and easy to understand Thanks!😍

[@brightsideofmaths]

You're welcome 😊

[@ああ-y9n8b]

Thanks from Japan.

[@LICHKING55Show]

Fantastic Tutorial!

[@biscuitsofdeath]

This is great. Way easier than creating separate matrices, but I see the value in knowing that you can multiply the inverse of elimination matrices to get a. Love the explanation, I found it easy to comprehend.

[@treckieeee5707]

Thank you for this. ✨

[@Mahfuj_Alam_Imon_]

It was really fun watching this video; now the concepts of LU decomposition seem pretty easy to me.

[@brightsideofmaths]

Nice :) Also watch the PLU decomposition then :)

[@guesmimontadhar7363]

Great explaination! Thanks a lot!

[@tekhal9779]

Thank you so much! It really helped me a lot

[@dahoyasmine2248]

Thank you so much, you have no idea how much this helped me !

[@rosemariemira1499]

Thank you so much! It really helped me a lot

[@goki8166]

u helped so a lot for my exam this video was so good the teacher showed the video to the whole class :D

[@brightsideofmaths]

Fantastic! You have a good teacher :)

[@deycitoloza7109]

¡Genial! Me ayudó mucho esta explicacion.

[@ammarabdelrazek5090]

Thank you, really helpful I have seen many videos but they were just more confusing Thanks again

[@brightsideofmaths]

Glad to hear that!

[@yozlemramadan4408]

The only video which helped me to understand now this works! Thank you :))

[@brightsideofmaths]

Glad to hear that!

[@rowansharaf8997]

Awesome explanation! God bless you!!

[@GandhiBoys]

Not all heroes wear capes ✊ Thank you!

[@Hnaiuoscefuobney]

Thank you very much from algeria 🇩🇿

[@satyaprakashpandit1936]

Concise , well explained, thank you.

[@brightsideofmaths]

Thank you very much for your support :)

[@anujnarode3315]

helped me a lot. Thanks

[@IMAHAPPYFATLARD]

Thanks!

[@brightsideofmaths]

No problem! And thank you :)

[@pedro_alonso]

Thanks from Brazil :D

[@malikialgeriankabyleswag4200]

Your workings are so efficient and elegantly presented. I love Germans lol

[@brightsideofmaths]

Thank you very much! :)

[@cissy27200]

Thank you omg !!

[@kundankrishna7467]

Very good explanation.

[@brightsideofmaths]

Glad you liked it And thanks for your support :)

[@elfarouk3306]

bro they should give you a nobel prize for that . thnx a lot

[@crazycrash1157]

Quick question if anyone knows it, why couldnt you put +2 or +4 in the L matrix because thats what happens when you multiply the negative in does it matter ? your teaching is so much more clear thanmy prof wish you were him doing good

[@brightsideofmaths]

You can do the matrix multiplication to check that you put the correct number into L!

[@hopelesssuprem1867]

Thank you so much for a such great explanation. This is the first video where I understood everything.

[@brightsideofmaths]

Great to hear!

[@hopelesssuprem1867]

@@brightsideofmaths do you plan to create a guide about svd decomposition? This will be an excellent addition to another decompositions

[@brightsideofmaths]

@@hopelesssuprem1867 Yes, I will do this in the linear algebra course :)

[@hopelesssuprem1867]

@@brightsideofmaths thank u so much. I will be waiting this a lot))

[@brightsideofmaths]

@@hopelesssuprem1867 At the moment, I have only a German video about this: kzbin.info/www/bejne/d4SclXmPmd6erZI

[@monsij2005]

Awesome explanation !!

[@brightsideofmaths]

Thank you!

[@sinecurve9999]

I am embarrassed to admit my University linear algebra course never covered LU decomposition. Gaussian elimination, yes. Super weird!

[@reiantaank3314]

Same. I'm encountering it for the first time in my masters

[@valawaters103]

could it be because your professor didn't consider it important? I mean if you can do the gaussian elimination maybe you do not need the LU decomposition (or maybe you do, i do not know i am still an undergrand)

[@PunmasterSTP]

How have your studies been going?

[@fruitygranulizer540]

because it is only needed if u are doing computational linear algebra. otherwise, gaussian elimination is much more practical.

[@agscholar21]

Man I love it when I find a video that explains something better than my professor😂😂

[@burakergocmen5661]

no need to another explanation. This is very good

[@sethproaps8899]

Thank you so much for this video. :)

[@오수진-r5f]

You're amazing!!! Thanks a lot

[@عباسحسنعلي-قسمالكهرباء]

Thank you very very very much

[@brightsideofmaths]

You are very welcome and thank you for your support ;)

[@yirokafalokarl-marx2008]

Thank you so much !

[@sivaramakrishnansubramania1956]

This is the quickest +complete primer to LU (and by extension LDU) decomposition

[@miroabdalian2114]

well explained, thx

[@ricegoing]

You're great ! vielen Dank

[@hakanozturk8367]

thank you.

[@duongmai1514]

Thank you!

[@ananthakrishnank3208]

Thank you!

[@devviz]

so the true purpose of lu decomposition is not necessarily to solve a matrix, but to demonstrate how gauss-jordan elimination method be performed?

[@brightsideofmaths]

"Solve a matrix" is not a common term. The LU composition is used to solve a system of linear equations.

[@khiemthongminh]

Thank you for the video.

[@xooldude]

Excellent teaching, pls make more of this content

[@brightsideofmaths]

Thank you, I will. I have a whole linear algebra course now that I will update in future! tbsom.de/s/la

[@xooldude]

@@brightsideofmaths thank you!

[@LeVraiment]

Thank you so much

[@NikitinBest]

PI-Sharaga and Vseleon loves you

[@larslagauw5452]

I failed my test because I didn't notice this is a tutorial for SQUARE MATRICES ONLY... Please put that in the title!

[@brightsideofmaths]

It's literally in the title written in the video at 0:14. Moreover, It's in the description and I also have a video about the PLU decomposition, which you can find in the pinned comments.

[@mustafamohammed8758]

Thanks, But can you look at the last ROW in the last step. You subtracted R(fourth) - 3R(Thired) from the ROW it will give us = 0, -3*, 0, -4 ...... The -3* make it wrong.(we should have 0)

[@brightsideofmaths]

Why do you think that?

[@kidymark16]

THANK YOU very much sir

[@cerenletonyada]

Very helpful thanks

[@dhananjaykupekar6892]

Concise and easy nice!!!

[@LocksVid]

thx bro

[@zathrasyes1287]

Could you make a good video about the incomplete LU decomposition?

[@shivanshiverma8025]

Bro, you are a savior! My teacher confused me like hell!

[@PunmasterSTP]

How have your studies been going?

[@bewyb323]

thank you!

[@allyourcode]

But... Why does this work? You keep writing an equals sign at the beginning of each line. Why are those equals signs correct? I understand for the first one, because obviously, A = IA, but for the rest, I am confused...

[@brightsideofmaths]

I would suggest that you just calculate the matrix multiplication on the right-hand side for each line :)

[@ashley0238]

omg the accent is so cute!!!! may I please know which accent is this?

[@brightsideofmaths]

:D It's German..

[@أوسكارأجدعفيلم-ي5ج]

انا و اخويا من مصر مزنوقين و بنحبك يا جينرال

[@narcisopaeste8985]

Wow. I am from India. This is very amazing I'm watching this for my girlfriend.

[@bense_tony]

Awesome man

[@zeustheboerboel3794]

I wish we had u in our university in India.

[@fresh7995]

how have u made it soo easy to understand lectures made it look like hell

[@farhanrafid8584]

Man, love you

[@ccbl6270]

thank you i get it

[@zhengyangsong]

Many thanks!!!!!!

[@brightsideofmaths]

You're welcome!

[@goose6258]

The matrices im working with always decompose into working with numbers that have decimals. This makes it really tedious. Is there an easier way to simplify matrices into LU when you are working with decimals?

[@brightsideofmaths]

Just post the example here :)

[@mirelaratu3113]

@@brightsideofmaths Please let me put an example of a matrix with fractions. I would like to understand how to solve it with this method. Thank you so very much! I'll write the following rows (7, 3, 1), (5, 3, 2), (4, 2, 2).

[@kimkim4232]

what if the question doesnt have a11 ? just y + z = 1 . there is no x . how to solve it?

[@ryanjackson0x]

Is it true that AEn=U, where En=L^-1?

[@bufdud4]

7:20 is wrong. You can't use the multiple of -3. That would not eliminate the fourth row. How did anyone not see that?

[@brightsideofmaths]

A rule of thumb: if you are the only one (out many people) who finds a very obvious mistake in a video, then it's quite likely that you are wrong. :)

[@bufdud4]

@@brightsideofmaths I saw my mistake. I thought the -9 looked like a -3, haha. Thanks for your easy explanation though!

[@brightsideofmaths]

Perfect! You are welcome :)@@bufdud4

[@arindamchak]

What if I take X2 = X2 + 2(X1) and keep 2 in the identity matrix column instead of (-2)?

[@haseebkhawaja1050]

No when we got the negative no. We dont add but subtract the negative no.

[@karmaakabane9727]

HI! I'd like to ask something, If one row tends to become all 0 when I tried an operation, does that mean I have to change rows before starting LU decomposition?

[@brightsideofmaths]

No, you can also check my video about the PLU decomposition: tbsom.de/s/ov

[@shohom350]

What to do when we have to switch two rows with each other.Urgent pls explain

[@brightsideofmaths]

See here kzbin.info/www/bejne/e2TGdIWZmat6o6c

[@shou-yickho2845]

im linking your utube channel on th bottom of my bacholers degree xD

[@ewesonlim2734]

May i know usually to get zero at row 2 first element, do we always refer to row 1 either by addition or subtraction? Or we can use row 3 or row 4 ?

[@ewesonlim2734]

ExSiZuGeSe thank you so much, yes you have answered my question completely

[@priyanshkumar17]

thanks !

[@brightsideofmaths]

You're welcome!

[@dreammyday5044]

what if I just use eliminating the first column and second column also got Zero?

[@helloyou4233]

awesome video