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LU decomposition - An Example Calculation 

The Bright Side of Mathematics
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📝 Find more material here: tbsom.de/s/ov
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Watch the whole video series about Linear Algebra and download PDF versions and quizzes: tbsom.de/s/la and tbsom.de/s/ala
There is also a dark mode version of this video: • LU decomposition - An ...
There is also a bright mode version of this video: • LU decomposition - An ...
To find the RU-vid-Playlist, click here: • Linear Algebra
Thanks to all supporters! They are mentioned in the credits of the video :)
There is a whole video series about Linear Algebra you should watch to understand the importance of the subject. I hope that it will help everyone who wants to learn about it.
This video is about the LU decomposition for square matrices. I show the algorithm with the help of an example.
I hope that it will help everyone who wants to learn about it. We discuss the whole Gauss algorithm for the LU decomposition. For any questions, please leave a comment or come to the community forum of the Bright Side of Mathematics: tbsom.de/s/community
#LinearAlgebra
#matrices
#Analysis
#linear
#Calculus
#Measures
#Mathematics
x
0:00 Introduction
0:33 Example
1:45 First step
2:41 Eliminating the first column
5:35 Eliminating the second column
7:10 Eliminating the third column
7:38 LU decomposition
(This explanation fits to lectures for students in their first year of study: Mathematics for physicists, Mathematics for the natural science, Mathematics for engineers and so on)
The Bright Side of Mathematics has whole video courses about different topics and you can find them here tbsom.de/s/start

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26 июн 2024

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Комментарии : 244   
@brightsideofmaths
@brightsideofmaths 3 года назад
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: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-E3cCRcdFGmE.html
@hardy4331
@hardy4331 3 года назад
I should be giving my university fees to this guy.
@MalamIbnMalam
@MalamIbnMalam 3 года назад
LOL I agree, it's shameful for what we have to pay for at Graduate school and Undergraduate
@eeshaanmj8656
@eeshaanmj8656 2 года назад
Then give
@STgauss3268
@STgauss3268 Год назад
Contribute him in steady...
@MisterAdri85
@MisterAdri85 3 года назад
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
@brightsideofmaths 3 года назад
Good luck tomorrow. Don't forget to cite me during the exam ;)
@MisterAdri85
@MisterAdri85 3 года назад
@@brightsideofmaths haha sure will !
@PunmasterSTP
@PunmasterSTP 2 года назад
How did your exam end up going?
@MisterAdri85
@MisterAdri85 2 года назад
@@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
@PunmasterSTP 2 года назад
@@MisterAdri85 That's awesome! How are you liking your third year?
@notgeo3912
@notgeo3912 2 года назад
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!
@jamespapakyriakopoulos6187
@jamespapakyriakopoulos6187 3 года назад
watched this video before my university lecture and it helped 10x more
@PunmasterSTP
@PunmasterSTP 2 года назад
How have your studies been going?
@agbandanalistowel4737
@agbandanalistowel4737 3 года назад
You're a genius man. You've saved me from long processes to go through. Thumbs up
@justakizuner6359
@justakizuner6359 2 года назад
This video is just what I need! Thank you professor!
@Dkdkxncnchz
@Dkdkxncnchz 3 года назад
u literally saved my life thank you so much
@guesmimontadhar7363
@guesmimontadhar7363 3 года назад
Great explaination! Thanks a lot!
@RobertMurphy-wm3ge
@RobertMurphy-wm3ge 3 года назад
Excellent explanation. Thank you very much
@rosemariemira1499
@rosemariemira1499 3 года назад
Thank you so much! It really helped me a lot
@LICHKING55Show
@LICHKING55Show 3 года назад
Fantastic Tutorial!
@kaif7312
@kaif7312 3 года назад
LOL, while my professor for graduate level algorithm course spent entire 2 1-hour lectures on explaining this.
@vychuck
@vychuck 3 года назад
Actually, your professor had to explain the foundation ogfGauss elimination to get LU done, i.e why you readily get this example.
@rowansharaf8997
@rowansharaf8997 2 года назад
Awesome explanation! God bless you!!
@treckieeee5707
@treckieeee5707 3 года назад
Thank you for this. ✨
@vfrostbane225
@vfrostbane225 Год назад
This was super easy to understand and explained so simply! Thank you so much!
@brightsideofmaths
@brightsideofmaths Год назад
Glad it was helpful!
@ne0fuze620
@ne0fuze620 Год назад
Thank you very much! This explained a lot
@MalamIbnMalam
@MalamIbnMalam 3 года назад
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
@PunmasterSTP 2 года назад
I'm just curious; who was your professor there?
@MalamIbnMalam
@MalamIbnMalam 2 года назад
@@PunmasterSTP Dr.Robert van de Geijn
@PunmasterSTP
@PunmasterSTP 2 года назад
@@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?
@PunmasterSTP
@PunmasterSTP 2 года назад
LU decomposition? More like "You are a man on a mission"...to spread knowledge and wisdom. Thanks again so much for making these videos!
@biscuitsofdeath
@biscuitsofdeath 9 месяцев назад
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.
@deycitoloza7109
@deycitoloza7109 3 года назад
¡Genial! Me ayudó mucho esta explicacion.
@moon_dragon22
@moon_dragon22 10 месяцев назад
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
@brightsideofmaths 10 месяцев назад
Thank you very much and thanks for the support :)
@vychuck
@vychuck 3 года назад
Done it really clear and accessible way
@esi5743
@esi5743 2 месяца назад
Great explanation! I very much appreciate your work.
@brightsideofmaths
@brightsideofmaths 2 месяца назад
Glad you enjoyed it! And thanks for the support!
@drioko
@drioko 4 месяца назад
the colors you use help me feel more relaxed and pay attention. good choice on the yellow and warm colors
@brightsideofmaths
@brightsideofmaths 4 месяца назад
Thank you so much 😀 Some people are annoyed by the bright colors such that I also offer dark version for all videos :)
@khiemthongminh
@khiemthongminh 3 года назад
Thank you for the video.
@pedro_alonso
@pedro_alonso 3 года назад
Thanks from Brazil :D
@user-vo6rc3xn6t
@user-vo6rc3xn6t 2 года назад
You're amazing!!! Thanks a lot
@timotheesamazingchannel3721
@timotheesamazingchannel3721 5 месяцев назад
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
@brightsideofmaths 5 месяцев назад
You're very welcome! :)
@ricegoing
@ricegoing 4 года назад
You're great ! vielen Dank
@anujnarode3315
@anujnarode3315 3 года назад
helped me a lot. Thanks
@nadew.02
@nadew.02 7 месяцев назад
Thank you so much. You saved me!
@brightsideofmaths
@brightsideofmaths 7 месяцев назад
You are welcome! And thanks for the support :)
@user-eg3pt2qg3v
@user-eg3pt2qg3v 4 года назад
Thanks from Japan.
@desmondtayes1812
@desmondtayes1812 4 месяца назад
i finally found what i have been searching for amoung 10 videos. thanks
@brightsideofmaths
@brightsideofmaths 4 месяца назад
Glad I could help :)
@satyaprakashpandit1936
@satyaprakashpandit1936 11 месяцев назад
Concise , well explained, thank you.
@brightsideofmaths
@brightsideofmaths 11 месяцев назад
Thank you very much for your support :)
@dhananjaykupekar6892
@dhananjaykupekar6892 3 года назад
Concise and easy nice!!!
@yirokafalokarl-marx2008
@yirokafalokarl-marx2008 3 года назад
Thank you so much !
@miroabdalian2114
@miroabdalian2114 3 года назад
well explained, thx
@cissy27200
@cissy27200 3 года назад
Thank you omg !!
@kidymark16
@kidymark16 3 года назад
THANK YOU very much sir
@Virglsgames
@Virglsgames 3 года назад
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
@zunkitgetu8042 3 года назад
well u write a perfect English but u didn't understand his words?
@Virglsgames
@Virglsgames 3 года назад
@@zunkitgetu8042Yes! Is it strange?
@vladimirsviridov3329
@vladimirsviridov3329 3 года назад
@@Virglsgames yes! ahaha
@bewyb323
@bewyb323 2 года назад
thank you!
@taruchitgoyal3735
@taruchitgoyal3735 11 месяцев назад
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
@brightsideofmaths 11 месяцев назад
Glad you enjoyed it! :) If it helps you, you can also watch my video about the PLU decomposition and download the PDF versions! :)
@taruchitgoyal3735
@taruchitgoyal3735 11 месяцев назад
@@brightsideofmaths Thank you. Can you also publish a tutorial on SVD-Singular Value Decomposition?
@brightsideofmaths
@brightsideofmaths 11 месяцев назад
@@taruchitgoyal3735 Yes, this will be part of my linear algebra series: tbsom.de/s/la
@kkkorobbb
@kkkorobbb 4 месяца назад
Thank you so much! Exam is tomorrow, and you just opened my eyes! It's amazing!
@brightsideofmaths
@brightsideofmaths 4 месяца назад
Nice :)
@Mahfuj_Alam_Imon_
@Mahfuj_Alam_Imon_ 7 месяцев назад
It was really fun watching this video; now the concepts of LU decomposition seem pretty easy to me.
@brightsideofmaths
@brightsideofmaths 7 месяцев назад
Nice :) Also watch the PLU decomposition then :)
@cerenletonyada
@cerenletonyada 2 года назад
Very helpful thanks
@saburirasheed4070
@saburirasheed4070 3 года назад
Thank you so much
@yozlemramadan4408
@yozlemramadan4408 Год назад
The only video which helped me to understand now this works! Thank you :))
@brightsideofmaths
@brightsideofmaths Год назад
Glad to hear that!
@farhanrafid8584
@farhanrafid8584 3 года назад
Man, love you
@monsij2005
@monsij2005 2 года назад
Awesome explanation !!
@brightsideofmaths
@brightsideofmaths 2 года назад
Thank you!
@duongmai1514
@duongmai1514 2 месяца назад
Thank you!
@dahoyasmine2248
@dahoyasmine2248 3 года назад
Thank you so much, you have no idea how much this helped me !
@hakanozturk8367
@hakanozturk8367 2 года назад
thank you.
@user-vk8jn5br1f
@user-vk8jn5br1f 7 месяцев назад
Thank you very very very much
@brightsideofmaths
@brightsideofmaths 7 месяцев назад
You are very welcome and thank you for your support ;)
@kundankrishna7467
@kundankrishna7467 8 месяцев назад
Very good explanation.
@brightsideofmaths
@brightsideofmaths 8 месяцев назад
Glad you liked it And thanks for your support :)
@bense_tony
@bense_tony 3 года назад
Awesome man
@ammarabdelrazek5090
@ammarabdelrazek5090 Год назад
Thank you, really helpful I have seen many videos but they were just more confusing Thanks again
@brightsideofmaths
@brightsideofmaths Год назад
Glad to hear that!
@ccbl6270
@ccbl6270 4 года назад
thank you i get it
@helloyou4233
@helloyou4233 4 года назад
awesome video
@goki8166
@goki8166 7 месяцев назад
u helped so a lot for my exam this video was so good the teacher showed the video to the whole class :D
@brightsideofmaths
@brightsideofmaths 7 месяцев назад
Fantastic! You have a good teacher :)
@IMAHAPPYFATLARD
@IMAHAPPYFATLARD 8 месяцев назад
Thanks!
@brightsideofmaths
@brightsideofmaths 8 месяцев назад
No problem! And thank you :)
@agscholar21
@agscholar21 Год назад
Man I love it when I find a video that explains something better than my professor😂😂
@zeustheboerboel3794
@zeustheboerboel3794 3 года назад
I wish we had u in our university in India.
@sabbirahmed3034
@sabbirahmed3034 2 года назад
Which software do you use to write and record videos?
@brightsideofmaths
@brightsideofmaths 2 года назад
Xournal and OBS
@hopelesssuprem1867
@hopelesssuprem1867 Год назад
Thank you so much for a such great explanation. This is the first video where I understood everything.
@brightsideofmaths
@brightsideofmaths Год назад
Great to hear!
@hopelesssuprem1867
@hopelesssuprem1867 Год назад
@@brightsideofmaths do you plan to create a guide about svd decomposition? This will be an excellent addition to another decompositions
@brightsideofmaths
@brightsideofmaths Год назад
@@hopelesssuprem1867 Yes, I will do this in the linear algebra course :)
@hopelesssuprem1867
@hopelesssuprem1867 Год назад
@@brightsideofmaths thank u so much. I will be waiting this a lot))
@brightsideofmaths
@brightsideofmaths Год назад
@@hopelesssuprem1867 At the moment, I have only a German video about this: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-AS9dFYdykw0.html
@malikialgeriankabyleswag4200
@malikialgeriankabyleswag4200 5 месяцев назад
Your workings are so efficient and elegantly presented. I love Germans lol
@brightsideofmaths
@brightsideofmaths 5 месяцев назад
Thank you very much! :)
@ewesonlim2734
@ewesonlim2734 4 года назад
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
@ewesonlim2734 4 года назад
ExSiZuGeSe thank you so much, yes you have answered my question completely
@LocksVid
@LocksVid Год назад
thx bro
@goose6258
@goose6258 3 года назад
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
@brightsideofmaths 3 года назад
Just post the example here :)
@mirelaratu3113
@mirelaratu3113 3 года назад
@@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).
@elfarouk3306
@elfarouk3306 3 года назад
bro they should give you a nobel prize for that . thnx a lot
@burakergocmen5661
@burakergocmen5661 3 года назад
no need to another explanation. This is very good
@xooldude
@xooldude Год назад
Excellent teaching, pls make more of this content
@brightsideofmaths
@brightsideofmaths Год назад
Thank you, I will. I have a whole linear algebra course now that I will update in future! tbsom.de/s/la
@xooldude
@xooldude Год назад
@@brightsideofmaths thank you!
@haifa6004
@haifa6004 4 года назад
VERY GOOD
@NikitinBest
@NikitinBest 3 года назад
PI-Sharaga and Vseleon loves you
@GandhiBoys
@GandhiBoys 3 года назад
Not all heroes wear capes ✊ Thank you!
@EnaifuosfecuoyneB
@EnaifuosfecuoyneB 4 месяца назад
Thank you very much from algeria 🇩🇿
@zhengyangsong
@zhengyangsong 3 года назад
Many thanks!!!!!!
@brightsideofmaths
@brightsideofmaths Год назад
You're welcome!
@sinecurve9999
@sinecurve9999 4 года назад
I am embarrassed to admit my University linear algebra course never covered LU decomposition. Gaussian elimination, yes. Super weird!
@reiantaank3314
@reiantaank3314 4 года назад
Same. I'm encountering it for the first time in my masters
@valawaters103
@valawaters103 2 года назад
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
@PunmasterSTP 2 года назад
How have your studies been going?
@fruitygranulizer540
@fruitygranulizer540 Год назад
because it is only needed if u are doing computational linear algebra. otherwise, gaussian elimination is much more practical.
@sivaramakrishnansubramania1956
This is the quickest +complete primer to LU (and by extension LDU) decomposition
@beytulk
@beytulk 3 года назад
Thanks bıro!
@zathrasyes1287
@zathrasyes1287 2 года назад
Could you make a good video about the incomplete LU decomposition?
@priyanshkumariitd
@priyanshkumariitd 3 месяца назад
thanks !
@brightsideofmaths
@brightsideofmaths 3 месяца назад
You're welcome!
@karmaakabane9727
@karmaakabane9727 8 месяцев назад
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
@brightsideofmaths 8 месяцев назад
No, you can also check my video about the PLU decomposition: tbsom.de/s/ov
@yabara_
@yabara_ 2 года назад
Wow!
@reamabdulsalam524
@reamabdulsalam524 9 месяцев назад
Hi is there any specific order I have to follow to convert the entries into zero ? Should I start from colum 1 from the left to the right from top to bottom or it doesn’t matter ? What if in one step I can convert two entries to zero ? How to place the k value in this situation ? I have this matrix and I have stuck 1,-2,2, second row 3,4,2, third row 1,-2,3 ! I could not find the answer in any of the websites please do explain in full , thanks
@brightsideofmaths
@brightsideofmaths 9 месяцев назад
Please check my Linear Algebra series where I explain the Gaussian elimination in all detail: tbsom.de/s/la
@user-gn3yw6bx2f
@user-gn3yw6bx2f 2 года назад
انا و اخويا من مصر مزنوقين و بنحبك يا جينرال
@narcisopaeste8985
@narcisopaeste8985 3 года назад
Wow. I am from India. This is very amazing I'm watching this for my girlfriend.
@arindamchak
@arindamchak 4 года назад
What if I take X2 = X2 + 2(X1) and keep 2 in the identity matrix column instead of (-2)?
@haseebkhawaja1050
@haseebkhawaja1050 3 года назад
No when we got the negative no. We dont add but subtract the negative no.
@jonfersarz3083
@jonfersarz3083 3 года назад
is it applicable on a non square matrix?
@brightsideofmaths
@brightsideofmaths 3 года назад
Yes! However, U is then the row echelon form in the end.
@larslagauw5452
@larslagauw5452 Год назад
I failed my test because I didn't notice this is a tutorial for SQUARE MATRICES ONLY... Please put that in the title!
@brightsideofmaths
@brightsideofmaths Год назад
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.
@ryanjackson0x
@ryanjackson0x 2 года назад
Is it true that AEn=U, where En=L^-1?
@kimkim4232
@kimkim4232 3 года назад
what if the question doesnt have a11 ? just y + z = 1 . there is no x . how to solve it?
@shivanshiverma8025
@shivanshiverma8025 3 года назад
Bro, you are a savior! My teacher confused me like hell!
@PunmasterSTP
@PunmasterSTP 2 года назад
How have your studies been going?
@eashankhan2048
@eashankhan2048 3 года назад
Hello I understood your method but what if we want to normalise U instead of L , i mean want if i want to have the 1s on the diagonal of U what should i do than. thank you, and great videos
@brightsideofmaths
@brightsideofmaths 3 года назад
If you want to get 1s in U, you just have to divide each row afterwards. This is indeed the simplest row operation :)
@zma_0878
@zma_0878 3 года назад
Geniusly
@dreammyday5044
@dreammyday5044 3 года назад
what if I just use eliminating the first column and second column also got Zero?
@shou-yickho2845
@shou-yickho2845 2 года назад
im linking your utube channel on th bottom of my bacholers degree xD
@fresh7995
@fresh7995 Год назад
how have u made it soo easy to understand lectures made it look like hell
@mustafakarakilic8111
@mustafakarakilic8111 2 года назад
what do we need to put in the L on the top triangle? cause it's empty?
@brightsideofmaths
@brightsideofmaths 2 года назад
Empty spaces only mean zero :) (It is not just laziness from my side but zeros will steal attention from the actual important stuff)
@littleastaroth4559
@littleastaroth4559 2 года назад
Is it just me or the last one should (-3) instead of 3 to cancel the -9 on the fourth row, or am i just wrong since i do 1st + 3rd row
@brightsideofmaths
@brightsideofmaths 2 года назад
You cannot use the first row to eliminate the -9 :)
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