QR decomposition (for square matrices)

Рет қаралды 100,739

4 жыл бұрын

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This video is about the QR decomposition for square matrices. I show the algorithm with the help of an example.
I hope that this helps students, pupils and others.
#LinearAlgebra
(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)

Пікірлер: 82

@brightsideofmaths Жыл бұрын

Download the PDF version here: tbsom.de/s/ov

@jabir5768 3 жыл бұрын

Finally someone that doesnt waste time, and shows clear precise explanations, thanks a lot

@alexman97412 3 жыл бұрын

I'm french and you are a german speaking english explaining this better than my teacher ... thanks

@brightsideofmaths 3 жыл бұрын

Thank you very much! I will also do some French tutorials in future :)

@rosarionight7633 3 жыл бұрын

A really nice explication for the theory behind the QR Method in Numerical Methods ! Thank you !

@PavelVlasak 3 жыл бұрын

Thanks, crystal clear and easy to understand explanation

@MattaparthiShivaBhargav Жыл бұрын

i love the energy and thankyou very much for explanation.

@indumathi5182 Жыл бұрын

Thanks a lot sir, I understood the actual meaning Gram Schmidt process as well as QR decomposition.

@vanhoa2856 2 жыл бұрын

so touching for an excellent video

@galeboetticher5373 3 жыл бұрын

This is Gold

@shyamyadav3163 3 жыл бұрын

Thank you so much. Your videos are awesome.

@moncef2733 3 жыл бұрын

I'm french, and I still can't understand the lack of explanation of my french teacher considering an english teacher just explained me way better how this works in 15 minutes than my teacher in 3 months. tysm ❤

@wailandaloussi9111 3 жыл бұрын

oui j'avoue en cours on comprend rien

@PunmasterSTP 2 жыл бұрын

How have your classes been going?

@richardzhou2659 4 жыл бұрын

Your videos are so nicely made I'm motivated to learn German just to understand some of them 😂. Hope you're well!

@luca7x689 3 жыл бұрын

Lol

@stryckeurs9250 Ай бұрын

Even if english isn't my native language so its a little bit complicated ur video is amazing thank you

@PunmasterSTP 2 жыл бұрын

QR decomposition? More like "This is excellent exposition!" Thanks again so much for all of these videos.

@zuper5842 3 ай бұрын

charro

@PunmasterSTP 3 ай бұрын

@@zuper5842What does that mean?

@lorenamamede8442 9 ай бұрын

Thank you so much!! Perfect explanation!

@brightsideofmaths 9 ай бұрын

Glad it was helpful! :)

@amaramar4969 5 ай бұрын

quick , clear and complete. Why doesn't my college prof explain like you? Thanks! I subscribed.

@brightsideofmaths 5 ай бұрын

Nice :)

@kautukraj 4 жыл бұрын

Very helpful!

@calinopincariu5530 3 жыл бұрын

Nice, thank you!

@ahsink.3080 2 жыл бұрын

Thank you so much, you really helped

@esi5743 Ай бұрын

Very helpful, thank you!

@brightsideofmaths Ай бұрын

Thank you for the support!

@larubiano0 Жыл бұрын

Thx, great help + easy explanation

@brightsideofmaths Жыл бұрын

Glad it helped!

@TheRojo387 Жыл бұрын

I read that this method is useful for finding the roots of polynomials via repeating the process to estimate limits that represent the eigenvalues of the equivalent matrix.

@user-hy5te5rf4b Жыл бұрын

realy good video thank you a lot

@umbranocturna6342 3 жыл бұрын

Helps a lot with my Exam preperations.

@PunmasterSTP 2 жыл бұрын

How'd your exams go?

@umbranocturna6342 2 жыл бұрын

@@PunmasterSTP barely passed

@PunmasterSTP 2 жыл бұрын

@@umbranocturna6342 Hey, a pass is a pass! How have things been going since then?

@strai5150 4 жыл бұрын

...yo bruh!! Stay safe from covid19✌️

@lancelofjohn6995 2 жыл бұрын

Thank you, your video save my exercise!

@brightsideofmaths 2 жыл бұрын

You are very welcome :)

@PunmasterSTP 2 жыл бұрын

How'd the rest of your class go?

@lancelofjohn6995 2 жыл бұрын

@@PunmasterSTP It goes well.:-)

@PunmasterSTP 2 жыл бұрын

@@lancelofjohn6995 I am glad to hear it!

@zubairshaikh7093 2 жыл бұрын

Thankyou Sir

@mathewalter 4 жыл бұрын

Many thanks for this inspiring and profesional talk. What software do you use for recording and writing?

@PunmasterSTP 2 жыл бұрын

I've seen him mention elsewhere that he uses Xournal.

@polarettoallasbugba 4 жыл бұрын

These videos are awesome, thank you for everything. Do you plan to translate your linear algebra series to English as well?

@brightsideofmaths 4 жыл бұрын

Yes, I am working on it :) kzfaq.info/sun/PLBh2i93oe2qtXb7O-kPaEhAtFEb3n9Huu

@Zikkiii 7 ай бұрын

thank you sosososo much😍

@brightsideofmaths 7 ай бұрын

You're welcome 😊

@Tarzan_of_the_Ocean Жыл бұрын

very good video🤝🙏👏

@user-wg5qp4zh5k Жыл бұрын

excellent video

@brightsideofmaths Жыл бұрын

Thanks :)

@hopelesssuprem1867 Жыл бұрын

I've just solved your last example and it was hard)

@petersagitarius4356 Жыл бұрын

please, do you have some url link to QR decomposition for non-sqare matrices ? (I read that QR is possible to apply for non-squared matrix also) Thanks.

@brightsideofmaths Жыл бұрын

It's not so different. Maybe wikipedia can already help you.

@mkt92z 3 ай бұрын

before normalizing, werent you suppose to divide by the dot product by ?

@yuyuhe9874 Ай бұрын

You are correct. But since q1 is normalized which makes its dot product equals 1, it is skipped.

@robn2067 4 жыл бұрын

Don't you have to consider the sign in front of scalar products in your R matrix?

@hamzahajjou5221 3 жыл бұрын

The matrix R contains scalar products only without the sign

@Baskakwiatkowska Жыл бұрын

Thank you!

@user-wg5qp4zh5k Жыл бұрын

Youre welcome!

@ukaszwysocki5790 Жыл бұрын

QR to tematycxny filmik

@brightsideofmaths Жыл бұрын

@@user-wg5qp4zh5k Indeed :)

@MrJeromelejeune Жыл бұрын

Hello, nice tutorial however, could you explain why signs are completly the opposite when we compute it on matlab? I had the same problem on an other matrice: A=[1 2 3;2 4 5;1 6 7], when I apply [Q R]=qr(A), it returns me some negative values in R matrix. By definition it shouldn't be possible... could you explain this please?

@brightsideofmaths Жыл бұрын

Which signs?

@sourabhsingh341 Жыл бұрын

Wie geht es ihnen!? I am new in Germany and loving this country

@syc8066 Ай бұрын

Would you consider doing a video on the SVD?

@brightsideofmaths Ай бұрын

Yes, that is the plan.

@bashiruddin3891 3 жыл бұрын

Inserts "Nooice" gif

@souadbougadi2417 2 ай бұрын

What is Q come the name what might for example décomposition of LU L lower U Upper

@brightsideofmaths 2 ай бұрын

Q could refer to "orthogonal matrix" where O is not used for obvious reasons :D

@DennisB1109 3 жыл бұрын

Why is a1 = 1? I thought a1 is the vector (1 1)

@PunmasterSTP 2 жыл бұрын

I think you're right; a1 is the vector (1,1). But after you normalize it and make q1, then the magnitude of that normalized vector is 1.

@medaphysicsrepository2639 Жыл бұрын

7:47

@brightsideofmaths Жыл бұрын

13:30

@medaphysicsrepository2639 Жыл бұрын

@@brightsideofmaths personal note bc I know im going to be coming back to this video again, great job

@brightsideofmaths Жыл бұрын

@@medaphysicsrepository2639 Ah, personal notes should note in public comments :) Nice that you can use the video. I also have a whole course about linear algebra: tbsom.de/s/la