QR Decomposition of a matrix and applications to least squares Check out my Orthogonality playlist: • Orthogonal sets Subscribe to my channel: / @drpeyam
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
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
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?
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
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.
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.
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
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?
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
This guy always leaves a smile on my face
Im at the point of the semester where I need to take whatever this guy took
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
Add Dr Trefor Bazett in that list. :)
3 hrs of lecture and i didnt understand a word.
5 mins of watching this video - and i undersand every thing !!
thank you.
You sir are a genius. This linear algebra extravaganza was super helpful!
Glad you like it 😄
And I thought it was something to do with QR codes :P
🤔😅😁😁😀
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
And the next decomposition should be the very important SV decomposition which one typically uses in the matrix product state formalism. :D
This is the funnest math tutorial video I've ever seen. You made the process seem so streamlined and easy, thank you!
This was expained so well that i understood despite i talk spanish and dont know even a little of english
Thank you for explaining a simple topic as it should be explained, in a simple way. Great explanation!
the radiance of his positivity in his teachings make me love linear algebra XD
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.
pleaseee in 03MIN.12 why the first resultat is 15/9 !!!
Your enthousiasm is amazing, the only thing that triggers me is that you put your line of your Q on the wrong side !
Enthusiasm increases by exp(2) when Watching it on 2x
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?
It doesn’t have to. For nonsquare orthogonal matrices we don’t always have Q Q’ = I, that’s only true for square matrices
omg you're so cute i can watch you teach all day
I wonder... Would a left-sided RQ decomposition ever be useful? And how easy is it to generate compared to QR?
Thanks alot!!!!!!!!!!!!!!!!!!!!! Prepare to hand in my homework set~~~~~~~
You're my hero!
I’m Captain Peyamerica! 🙂
omg, thank you a lot for your priceless knowlage
t amo gringo, entendi como el putas no mk lo amo me ayudaste a estudiar para el parcial no nea feliz
Thanks so much for explanation, It was clear and concise and to the point.
Good video! I looked very good. What do you think of Jimmy Hendrix? If you like my guitar and harmonica you will be happy.
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
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
Thank you so much. This really helped my understanding of qt decomposition
u are like the bob ross of math :) thank you
This tutorial is amazing, thank you
Thankyou for being successful in successfully wasting my time
Awww you’re welcome!!
Best QR decomposition video I've found. Well explained, straight to the point, easy to understand. Thank you.
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.
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.
@@sandorszabo2470 Finally someone understands me :D
I totally agree
Eh useless semantics
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
God Bless you, man!
3:16 what does he mean here? what is rescaling a vector ? just getting rid of the denominator ?
Multiplying by a constant, here so that the components are integers
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?
thank you great video
Great video man
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
You divide by the length of the vector to get a unit vector
@@drpeyam I just understand that numerator 1 is part of the formula right ? that was my question . 😄
The best explanation given on this topic!
WOW this was explained really well, I wish my professor could teach like this :(
Thank you sir.
Thank you so much. Very helpful
Glad it was helpful!
The watch steals the show
Thank you sir👍
How about its importance in finding evalues?
Dr Ariya from Krish
Do you have videos on SVD? Thanks for this video
What is the application of QR decomposition?
I want to kiss him :*
Awwwwww!!!
6:50 known Q find R
Do 100 integral challenge!!!
There’s already a 100 T/F challenge
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?
No, u2-u2hat is perpendicular to v1
man how did i not find you before, you're litteraly going to make me pass numerical analysis
IR=V fin.
「動画の音が良くない」、
Thanks a lot for your clear explanation!
Your V's look exactly like your U's
Very useful session thank you so much ❤
I have been struggling with this topic, you explained this so well. Thank you!
WOW THANK YOU DR. YOU ARE THE BEST
Thanks a lot!! The example was very illustrating!
Wow best explanation and nice style of teaching. Very precise and easy to understand
I wanted SVD and two grid method too :)
This was really good :)
First uwu!
Thanks you for an amazing explanation!
A nice lin alg video again. I hope my students will also like it 😊
What a living legend... Amazing Peyam
thank dr peyam! I really liked the extension to least squares in the second half of the video.
crazy good, thank you
08: 10
Great explanation, thanks!
Dr Peyam.. can you please explain what LU decomposition is.. I kind of noticed in my textbook... but no idea what it is..
There’s a video on that
@@drpeyam Ok thanks... I'll check it out
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
It’s an Invicta watch, you can get it on amazon
@@drpeyam Thanks for letting me know!
Perfect explanation. Thx professor
I love this man
Could you do QZ decomposition.
THANK YOU SO SO MUCH
absolutely fantastic
Thanks! Sir
thx bro !!
very very clear
good job peyam
Great!
thanks for your work.
Foi muito útil! Thank you so much!
Do you put the slash in the wrong place in "Q" just annoy viewers like me!?
No, that’s just the way I’m used to writing it
@@drpeyam fair enough
@@typo691 he is left handed so its easier to swipe down and away