QR decomposition

QR Decomposition of a matrix and applications to least squares
Check out my Orthogonality playlist: • Orthogonal sets
Subscribe to my channel: / @drpeyam

[@riccardocapellino7680]

This guy always leaves a smile on my face

[@dani21534]

3 hrs of lecture and i didnt understand a word. 5 mins of watching this video - and i undersand every thing !! thank you.

[@quamos99]

You are on my elite teachers list: Sal from Khan academy, The organic chemistry tutor, Professor Dave, and now Dr Peyam. Hats off to all of you for making my university life easier. Massive respect and love for all of you

[@Rwko.]

Add Dr Trefor Bazett in that list. :)

[@ARNAKLDO]

You sir are a genius. This linear algebra extravaganza was super helpful!

[@drpeyam]

Glad you like it 😄

[@OrdinaryXtreme]

This is the funnest math tutorial video I've ever seen. You made the process seem so streamlined and easy, thank you!

[@NayaM0]

Best QR decomposition video I've found. Well explained, straight to the point, easy to understand. Thank you.

[@abnerandreymartinezzamudio3366]

Im at the point of the semester where I need to take whatever this guy took

[@vassisn2001]

Thank you for explaining a simple topic as it should be explained, in a simple way. Great explanation!

[@elonmusk7142]

That's awesome. I don't understand matrix and I don't understand english but with your funny explinations, I understand everything. Thank you so much.

[@springnuance7048]

the radiance of his positivity in his teachings make me love linear algebra XD

[@GangerPlayz]

This was expained so well that i understood despite i talk spanish and dont know even a little of english

[@judesharp6472]

man how did i not find you before, you're litteraly going to make me pass numerical analysis

[@Ajay-xd7zq]

Thanks so much for explanation, It was clear and concise and to the point.

[@dengdengkenya]

The best explanation given on this topic!

[@peytonv.6614]

I have been struggling with this topic, you explained this so well. Thank you!

[@stekim]

thank dr peyam! I really liked the extension to least squares in the second half of the video.

[@samytee3282]

Wow best explanation and nice style of teaching. Very precise and easy to understand

[@samytee3282]

I wanted SVD and two grid method too :)

[@吳弘叡]

Thanks alot!!!!!!!!!!!!!!!!!!!!! Prepare to hand in my homework set~~~~~~~

[@epiccheeseburgercat]

Thank you so much. This really helped my understanding of qt decomposition

[@Bombelus]

You're my hero!

[@drpeyam]

I’m Captain Peyamerica! 🙂

[@fatty3910]

omg you're so cute i can watch you teach all day

[@jxw7196]

What a living legend... Amazing Peyam

[@joaofernandes8051]

And I thought it was something to do with QR codes :P

[@vijayank1170]

🤔😅😁😁😀

[@IlMarinz]

I've Always seen matrix decompositions (QR, LU) done with square matrix, it's a bit strange for me to see them in the nonsquare world. Also, I was told that Q must be Unitarian and Hermitian (I guess for IR orthogonal and symmetric would be fine) hence making QR only be possible in square matrices by definition. I wonder how much of a lie resides in what I just told

[@FunctionalIntegral]

And the next decomposition should be the very important SV decomposition which one typically uses in the matrix product state formalism. :D

[@kyliemun2681]

God Bless you, man!

[@RiVaLBrite]

WOW this was explained really well, I wish my professor could teach like this :(

[@TheInuyashaGuy]

This tutorial is amazing, thank you

[@holyshit922]

Gram Schmidt is good for paper and pencil calculations but i heard that it is numerically unstable and I should avoid it when I write program for QR decomposition Householder reflections or Givens rotations are better choice for those who want to write a program Silly , or maybe not in Householder reflections we need transpose of matrix to get Q and square matrices are easy to transpose in place Transpose of rectangular matrix also can be done in place but it is not so easy

[@enamanjgo8930]

u are like the bob ross of math :) thank you

[@BloemkoolGaming]

Your enthousiasm is amazing, the only thing that triggers me is that you put your line of your Q on the wrong side !

[@chiragmittal3313]

Enthusiasm increases by exp(2) when Watching it on 2x

[@Mr.HugsHoney]

WOW THANK YOU DR. YOU ARE THE BEST

[@gulrukhsor_akhmadjanova]

omg, thank you a lot for your priceless knowlage

[@paultaufalele1821]

Thank you so much. Very helpful

[@drpeyam]

Glad it was helpful!

[@unruly_ronin]

Great video man

[@sandorszabo2470]

A nice lin alg video again. I hope my students will also like it 😊

[@carlosalbertodelgadoelizon4457]

Thanks a lot!! The example was very illustrating!

[@zonglehuang4147]

Thanks a lot for your clear explanation!

[@syedmuhammadabdullah2920]

Thankyou for being successful in successfully wasting my time

[@drpeyam]

Awww you’re welcome!!

[@joaomorais6101]

Perfect explanation. Thx professor

[@dariusfoodeei8181]

I love this man

[@ankitb3954]

The watch steals the show

[@MrRyanroberson1]

I wonder... Would a left-sided RQ decomposition ever be useful? And how easy is it to generate compared to QR?

[@virgenalosveinte5915]

thank you great video

[@Elisko245]

Thanks you for an amazing explanation!

[@arwatawfiq4088]

Very useful session thank you so much ❤

[@harshala5385]

Thank you sir.

[@059812]

Great explanation, thanks!

[@abdelrhmandameen2215]

absolutely fantastic

[@JohnDoe-sc4zf]

Hey, thanks for the amazing video. I just have one quick doubt. As you said Q is orthonormal matrix, then when I compute Q*Q' it does not give I. Please enlighten me, or am I misunderstanding something?

[@drpeyam]

It doesn’t have to. For nonsquare orthogonal matrices we don’t always have Q Q’ = I, that’s only true for square matrices

[@humanwang9854]

Thank you sir👍

[@Matrioshka_Brain]

This was really good :)

[@kevinshao9148]

thanks for the video! but one question, even if R' is not invertible (meaning A has linear dependency) , there still solution for LS right? just lose one dimension. No?

[@rampage14x13]

Thanks this video series has really been helpful! Also, just wondering if you would be willing to share but I was wondering what watch you're wearing? I think it looks great

[@drpeyam]

It’s an Invicta watch, you can get it on amazon

[@rampage14x13]

@@drpeyam Thanks for letting me know!

[@marce3893]

thanks for your work.

[@kyc3722]

very very clear

[@a.s.6898]

crazy good, thank you

[@yapzhilin9857]

THANK YOU SO SO MUCH

[@DSKim-ej5uf]

Good video! I looked very good. What do you think of Jimmy Hendrix? If you like my guitar and harmonica you will be happy.

[@eduardamachado7687]

Foi muito útil! Thank you so much!

[@aminfadaei4056]

good job peyam

[@mohammadburhanmanzoor3806]

How about its importance in finding evalues?

[@ReversePrimeOFFICIAL]

Do you have videos on SVD? Thanks for this video

[@ademalliche878]

pleaseee in 03MIN.12 why the first resultat is 15/9 !!!

[@RenegadeFury]

I thought u2 hat was perpendicular to V1, but apparently that's what v2 is? Or is u2 hat supposed to be parallel to V1?

[@drpeyam]

No, u2-u2hat is perpendicular to v1

[@Handelsbilanzdefizit]

What, if you define a kind of Matrix-Product with the compositon of the elements: A = { {a11(x), a12(x)},{a12(x), a22(x)} } and B = { {b11(x), b12(x)},{b12(x), b22(x)} } So that, A°B = { { a11(b11(x)) + a21(b12(x)), a12(b11(x)) + a22(b12(x)) }, { a11(b21(x)) + a21(b22(x)), a11(b21(x)) + a21(b22(x)) } } Linear Algebra is boring, because I never understood it well. Make more videos about this crazy fractional calculus stuff! Something like this: (d/dx)^f(x) x = f'(x), where f(x) is the order of the derivative. Or functions that transform other functios to their derivatives: g1(f(x)) = f'(x), g2(f(x))= f"(x), ... where gn depends of (d/dx)^n f. Then you could "maybe" generalize derivatives by these functions --> g0.3(f) = (d/dx)^0.3 f

[@kolinnhtooaung2408]

Thanks! Sir

[@ninisky2706]

3:16 what does he mean here? what is rescaling a vector ? just getting rid of the denominator ?

[@drpeyam]

Multiplying by a constant, here so that the components are integers

[@huongtran7922]

What is the application of QR decomposition?

[@phantom8673]

in W1 , where did you get 1/3 ? and what is W1? you said its the lenght of vector[2 2 1] it should be 3 . but why its 1/3?? i dont get it

[@drpeyam]

You divide by the length of the vector to get a unit vector

[@phantom8673]

@@drpeyam I just understand that numerator 1 is part of the formula right ? that was my question . 😄

[@rasikajayathilaka3516]

Great!

[@sabbaramine2719]

thx bro !!

[@counterko]

6:50 known Q find R

[@mzeeshanzafar28]

Dr Ariya from Krish

[@vijayank1170]

Dr Peyam.. can you please explain what LU decomposition is.. I kind of noticed in my textbook... but no idea what it is..

[@drpeyam]

There’s a video on that

[@vijayank1170]

@@drpeyam Ok thanks... I'll check it out

[@7amood40]

Could you do QZ decomposition.

[@Rundas69420]

Orthogonal Matrices are a bit strange anyway. I will never understand why you call a Matrix with orthoNORMAL column-vectors orthoGONAL and not orthonormal. Most of the time I love maths, but sometimes I hate it xD.

[@sandorszabo2470]

I agree with you. Luckily, there is a book where authors say orthonormal matrix. In my lectures I also say this. And there are other cases where I use the corresponding correct name. Similar, more terrible thing is 😄 "this infinite series is convergent". Math is nice, but the language created by persons is not necessarily correct.

[@Rundas69420]

@@sandorszabo2470 Finally someone understands me :D

[@drpeyam]

I totally agree

[@HilbertXVI]

Eh useless semantics

[@1.4142]

IR=V fin.

[@3ia18_prasetyaharkrisnowo7]

Do 100 integral challenge!!!

[@drpeyam]

There’s already a 100 T/F challenge

[@deniztunayildiz4518]

08: 10

[@deepgems2246]

Your V's look exactly like your U's

[@junior-ee5dm]

t amo gringo, entendi como el putas no mk lo amo me ayudaste a estudiar para el parcial no nea feliz

[@typo691]

Do you put the slash in the wrong place in "Q" just annoy viewers like me!?

[@drpeyam]

No, that’s just the way I’m used to writing it

[@typo691]

@@drpeyam fair enough

[@Sup3rlum]

@@typo691 he is left handed so its easier to swipe down and away

[@jiongt2677]

「動画の音が良くない」、

[@shokan7178]

First uwu!

[@esutana]

The math people call this Q is semi-orthogonal matrix. They define that orthogonal matrix must be square. en.wikipedia.org/wiki/Semi-orthogonal_matrix