LU Decomposition - Shortcut Method
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- Опубликовано: 12 сен 2024
- This video explains how to find the LU Decomposition of a square matrix using a shortcut involving the opposite of multipliers used when performing row operations.
Site: mathispower4u.com
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Mate, i cannot stress how easy you have made this topic to comprehend. I am comfortable in this topic thanks to you!
That is great! Thank you for letting me know.
Mathispower4u Same here, Thank You!
I'm really so thankful to him, thanks ^_^
Thank you so much.
@@Mathispower4u Thank you!
I'm sorry but I watched every other videos about this topic but this guy taught it to me in less than 4 minutes...DAMN
Finally, a humanly appropriate tutorial on LU decomposition! Thank you!
The best way is to visit the mathispower4u website. It has all of the videos in order by course and topic.
You're the man. I've been following you for 3 years now.
Thank you!
Is LU Decomposition the same as LU Factorization?
Yes
I've spent more than an hour looking for some clean explanation about LU decomposition in my own language for my uni exam. After swearing... a little... and increasing my hatred towards my country I found your tutorial and you made me understand this whole thing in less than 6 minutes. Thank you!
Almost 8 years and i can't thank you enough, great job.
The best video on LU decomposition. Thank you
Best video I have seen on this topic so far! I am lecturing an undergraduate math course this semester and you have just helped make it easier for me to explain the LU decomposition algorithm to my students. Thank you!
donbradman334 I should also point out just for interest that I am using a combination of your method and that in chapter 2.5 of Lay's linear algebra book to explain this to the students.
What took me hours to understand has just been demystified in 10min! You're amazing, I can't thank you enough!!!
thx, nice explanation
Wow, you made this extremely easy to follow and comprehensive. I can't thank you enough!
😊😊😮😊m KK😊l
I have a midterm in 3hrs and this was very helpful indeed. Other youtube videos were really confusing
OMG this is the best explanation i could've found.You Successfully explained CLEARLY and SIMPLY the LU method whereas i've benn struggling for one month to understand the complicated lecture given by My teacher on this Topic at my Engineering School.Thank you so much Sir for the Great Job you've done .
THANK YOU!!!! I have spent hours on trying to figure this out and you made it easy to learn in 10 mins. Great video!!!
I don't always comment but when i do, it is worth commenting. THIS IS BRILLIANT!!!
I've been watching your videos for a year and you saved my cal3 and linear algebra. Thank you!
You've helped me through all of my undergrad. THANK YOU.
I can't believe how easy you made this lesson. All these other videos I watched just complicated my morning, but THANK YOU very much!
Man! this is awesome. We get 4x4 or higher order in exams and it would take forever. Thanks for your help.
It felt like a pump of info before my quiz. Seems like you've been helping people like me for many years. You must have a vip place in heaven
HOLY SHIT I'VE BEEN CRYING OVER NOT BEING ABLE TO DO THIS FOR 2 HOURS AND YOU JUST SAVED ME THANK YOU!
I couldn't understand this concept anywhere else before I saw this video. thank you so much!!
this is by far the most concise and informative video of lu decomp. ive seen.
Thank you so much.
this the best video I saw on RUclips. I have been looking for hours.
Wow, thanks!
Thanks for making this video! Simple to remember!
thank u thank thank u soooooo much after 11 years u are such a legend
Thank you for taking the time to leave a comment. I am glad I could help out. 😃
Super method!!!
I was not able to solve LU decomposition till now.
This will help a lot.
Glad to know I could help!
Before seeing this video I was like "I'll never understand in my entire life" and after your explanations "it was easy af" ... thank u so much bro
Great video. My university should be paying you to teach me, not my Numerical Analysis and Computing Professor. Thank you!
same, my numerical methods professor sucks
fra ti metterei mi piace ma cazzo stai a 69 non posso rovinarlo
Seriously thank you so much !!!! your explanations are clearer than a teacher with a PHD !!!
You explained this 100x better than my instructor. Straight forward without meaningless definitions
I watched your video and it was self explanatory.I tried to watch another video to compare but I think you gave explanation to why the elements in the L matrix were so.Thank you sir.
Just one question. Say, in the first step, R22 becomes 0. What will you do in the third step then? Would you say that LU decomposition doesn't exist?
I was a little confused when my instructor was teaching this. My textbook wasn't that clear either. Now, I understand it. Thanks for posting this video about how to do it.
Thank god someone other than my professor can teach this. You are helping me get a better grade on my final.
Clear and lucid, thanks.
May I ask, what software and peripherals (mouse, stylus+pad, ... ??), and the OS you used to make your presentation?
Thanks a lot! I've been struggling on this for a long time.
Im wondering about this too... And are we only allowed to multiply one of the row only? Like is 2R1+3R2 allowed? if it is, which number should we plug onto the L? -2? -3? -2/3? -3/2? will all give the same answer?
Are there some matrices wherein this is not applicable? It doesn't seem to be applicable on this matrix im working on
Thanks so much! Best video I was able to find on LU factorization
Thank you both for your help in understanding the idea and for your providing of this practical method of implementation! Much more clear than university material...
I just have one question...why does A need to be able to be reduced to U without row interchanges? Since this is also a row operation, that's not clear to me. Does this mean that, in practice, I cannot use techniques like Gauss pivoting to obtain U?
Sorry but I am pretty much a beginner in this field...
thanks a lot i wasn't able to understand LU decomposition from Meyer book but U solve this problem for me!
Beautifully presented. Completely demystified what had previously been quite confusing. Thank you!
THANK YOU! I appreciate it! This saved me right before my exam =)
Thanks Man 👍🙏. Thank You for making it this easy and Understanding.
thank you a lot man, this is how you explain a method
Thank you so much you dnt understand how easy you made this to understand
A great video explaining the shortcut method for LU decomposition.
Thank you so much. I think there is a need to make a revolution in university degree. RUclips lessons are far more efficient than stupid useless 3 hour lectures.
Makes much more sense now. thanks for the video !!
great was searching for a good explanation and example, and here i found it. tyvm
Thanks for the tutorial. I found it helpful. Oh, by the way, does this method work with 4x4 matrices as well?
Thank you for making this concept easy to understand. You are a Godsend for students like myself.
You are so welcome!
you saved me with that explanation man! greetings from brazil!!
dude this clip is AWSEOM!!!!! now Ive got idea of this topic.
thx for this amazing vid
greetings from Seoul
Writing my final paper for numerical methods tomorrow, this really helped a lot! Thanks :)!!!!!
This is now infinitely easier to understand
Thank you so much! its the best video in all youtube for this topic! you made it super easy to understand!
Saved me from soooooo much extra work thank you!
You made me understand it, superb person.
I'd like to thank you for your easy and clear explanation, and I have a question:
Can I use any row to obtain the "zeros" ?
As per my understanding is Yes, as every row represents an equation, so I can use any row to obtain the zeros, I'd like you to confirm.
Thanks in advance.
Its 4 am now and i am watching this finally i learned thank you sir.
Thank you for the simple explanation, helped me wonders!
I clocked out in class for some dumb reason. Thank you for your help.
Very helpful. Thank you again James.
Really good explanation!! Thank you!
what if we have 0 as one of the elements in the original matrix A as one of the elements?....What value do we store in the lower triangular matrix in its place?
0, for those that are also curious.
then you should multiply by 0, and find the summation of whatever the row is with zero, which would give you the same original row, then you'll but that zero in the lower matrix, I guess this is the way :)
THIS IS COOOL WELL DONE!! Now it's easy to understand! Thank you!
Great! I added it to a playlist to watch later if i ever need
saves a lot of time. do you have a video (or some pdf/website on the internet) that proves why this works? I'm not allowed to use unproved algorithms. thanks.
Best explanations EVER!
Thank you tomorrow i have exam this video is very good to explain LU
Exam in 1 hour. You saved my life!
Very simple and concise !
Thank you very much.
Thank you for this very beautiful way of explanation s......
You teached me this method better then my teacher.Thank you a lot.
Thank you! In this time of pandemic 2021, our professor doesn't teach us. We tuition fee in this subj should go to you instead of my university.
Finally understood 😭🙌. Thank you!
So easy to do these now :o
Thanks so much
Thank you SO much for this video. I understand it much better now. I really appreciate it :)
thank you so much, this video help me alot clearing out confusion.
great video dude, you help me alot
Very good explanation! A question: Does this shortcut method work for all square matrices? For example in the case of the previous video where you showed how to do LU decomposition using elementary matrices, the last row operation consisted of multiplying row 2 by 4 and adding it to 5 times row 3. What would be the multiplier for the shortcut method in this case?
For anyone wonder why L consists of 1's on the main diagonal (and not any other non-zero number).
*_Note_* : There is a short answer, and further explanation (so don't feel overwhelmed by the length of the comment :) )
short answer: because we assumed A can be row reduced to U with *only* subtracting a multiple of a row from a row below it. (1)
long explanation (take a pencil and paper to follow along :) ):
How does this imply that L has only 1's on the main diagonal??
Recall that what are we actually doing when reducing *A* to *U* is described with the equation:
*E1 E2 E3 ... Ek A* = U , where *Ei* are elementary matrices
So, by our assumption (1) , all *Ei* have 1's in the main diagonal and are lower triangular (think about that for a sec.)
We have *L* =inv( *Ek* )...inv( *E1* ) (2)
But note that inv( *Ei* ) is also lower triangular with 1's in the main diagonals (think about this for a sec.-- hint: what elementary matrix type is *Ei* ?)
Moreover, if M = inv( *E2* ) * inv( *E1* ) then M is lower triangular with 1's in the main diagonal (think about that for a sec.) From this realization, you can think about how the rest of the multiplications in (2) will not change the property that the product is lower triangular and has 1's in the main diagonal.
Therefore, *L* is lower triangular with 1's in the main diagonal.
I hope this helps clarifying the question a little bit. I know it might be hard to follow the argument especially that I'm typing in RUclips with minimal formatting :).
Thanks....you made it easy for me...
Thank you brother.Great solution.
interesting, that ,when teachers give us the explanations of something like that, it looks super hard, but then you watch it here, on youtube, and you realize, it's actually quite eazy to understand
+SooZoodimp well some you're make harder but looking around you found some who make simple for us.. that's why is not fair the education system since we all learn different.
thank you sir today is my papr and i got useful tricks...thanks alot
Wow.. Wonderfully explained.. I wrote a program in R following your instruction.. came out great. One question .. when you pick up a multiplier (eg.. on a 3*3 matrix as your example) when you are on row 3 column 2 .. should we necesarily choose the row above or just any row above.. I initally programmed to always factorize from Row1.. but it did not work out.
You are a hero bro
good n really easy way u made us understand it
Cheers , I was trying to fix one of the equations since 3 hours, but have had no luck. I found this is very helpful Awesome explanation , Cheers mare :) :)
Masum Billah i know right, freaking sometimes takes whole to do it😂.
What if we don't need 3 operations to obtain U? In that case, what should we put in for the last blank in L?
I assume 0, if you mean that there is already a zero there in the upper matrix
damn, this made LU's so much easier. cheers!
Great work sir, it worth working
the quote at the end just changed my life...
I have an exam in 15 hours, you just saved my ass XD
Incredible, looks so easy now... Thank you !!!
I wonder how the hell does my lecturer spends 2 hours on this and noone still gets it, while this dude does it in 5 minutes