Givens Rotation Method

[@raoulfrank6606]

These videos are single-handedly pulling me through my numerical computing class in uni. Such a gem. Thank you.

[@isaacamornorteyyowetu]

Waow. It's a pleasure

[@ricardoraymond9037]

The great thing about your tutorials is you use matrix enteries of rows and columns to show the concepts unlike others who only use matrix symbols like AA^T etc to explain which turns out more confusing. You have the correct approach!

[@isaacamornorteyyowetu]

Thanks for the feedback. I'm happy to hear that.

[@godvana1017]

Out of all the videos I have watched yours is the first one that really made me understand this rotation method for my upcoming exam. Really really well done, simple and straight to the point of how its done. Thank you so much and greetings from Germany!

[@isaacamornorteyyowetu]

Thanks for the feedback

[@itsmidonah]

best internet teacher in this section, thank u

[@isaacamornorteyyowetu]

It's a pleasure. Thanks too for the comments

[@fatimaginebra7884]

Thank you! This is the only step-by-step that actually explains doing QR through Givens Rotation. Thank you!

[@isaacamornorteyyowetu]

Glad it was helpful!

[@AlexAlex-cl4tz]

I found a typo on 5:19 in matrix G2 (last row c and s need flip)

[@isaacamornorteyyowetu]

I see.Thanks so much it is really a typo.

[@davidcarausu9256]

I am gonna tell my grandmother to pray for you !

[@isaacamornorteyyowetu]

Thanks

[@bigenimanajeanclaudebezale2814]

Thanks for this detailed and easy to understand example

[@isaacamornorteyyowetu]

Glad it was helpful!

[@Thesavage235]

Thank you very much! This video helped me a lot.

[@isaacamornorteyyowetu]

Glad it helped!

[@hieuletrung2515]

This really helps me, easy to understand

[@isaacamornorteyyowetu]

Thanks for the great feedback. Well appreciated. Kindly subscribe, like and share with friends.

[@grs3579]

love your work, easy to understand

[@isaacamornorteyyowetu]

Happy to hear that!

[@user-pj7ch2rk6l]

Good job!

[@isaacamornorteyyowetu]

Thanks

[@mathematicslessonsandtutor8006]

Thank you for this video

[@isaacamornorteyyowetu]

My pleasure

[@zz2729]

Thank you！ Your video helps me a lot!!!!

[@isaacamornorteyyowetu]

Glad it helped!

[@marinabastos2630]

Thank you for the explanation! This helped me!

[@isaacamornorteyyowetu]

I'm also glad! Thanks for the feedback

[@kwesia.ohene-obeng4503]

How do you choose the position of c and s at each stage?

[@isaacamornorteyyowetu]

With reference to the Gives' Matrix, we always have a square matrix. The c's will be along the diagonal and the s will be along the off-diagonal. If you take notice, the c's are attached to the x's selected and the s's are more attached to the y's we want to delete. Then the position of both x and y in the matrix will influence us on how to position the c's and s's. I think this explanation helps. Sorry for the late reply. :) There is actually a typo at 5:19. Thus G2. Thanks.

[@ShubhamKhandelwalmam]

outstanding lecture.

[@isaacamornorteyyowetu]

Many thanks. That's great to know.

[@restacks8777]

Very helpful, thank you

[@isaacamornorteyyowetu]

Glad it was helpful! Kindly share it with friend. God bless you.

[@ahmedainancheh7451]

easy to understand . thank you very much

[@isaacamornorteyyowetu]

Thanks for the feedback.

[@muzuriaimable9581]

Thank you for your explanation bro

[@isaacamornorteyyowetu]

That's great to hear.

[@ticimici.]

thanks bro

[@isaacamornorteyyowetu]

Welcome

[@virginieyoukoudjou1657]

Thanks for the video. by the way there is a little mistake in the answer of G1.A1. The -1 should be on the last row and not the row before

[@isaacamornorteyyowetu]

Ok. Thanks. That's typing error.

[@jacobclinton9849]

Where did the R matrix at the end come from, and how do I work it out.

[@isaacamornorteyyowetu]

We obtained that from G3*A3. I believe the explanation helps.

[@nobodyreally1634]

Thanks for this very helpful video. One thing that is still unclear to me however, how do you choose x?

[@isaacamornorteyyowetu]

x is the pivot element. Once x is chosen, it means y, an element beneath this x will be deleted when selected. I believe the explanation helps!

[@dmit10]

It would be nice if you could demonstrate this method on a companion matrix. It's an interesting idea to compute polynomial roots.

[@judas6726]

What if our matrix is a 3x2?

[@ttl8301]

Can you explain more in detail how or why you know to pick x and y, and how you know the placement of c,s,-s and c for G1, G2 and G3.

[@isaacamornorteyyowetu]

x a pivot element and y is any number beneath the x and you intended to make 0.

[@tudormarian4916]

What elements change by multiplying a square matrix on the left by a Givens plane of rotation? Argue.

[@isaacamornorteyyowetu]

All the elements in the resulting matrix change. But is worth noting that the y value chosen to construct the givens rotation matrix runs to zero after the multiplication.

[@isaacamornorteyyowetu]

I hope the explanation above helps?

[@tudormarian4916]

@@isaacamornorteyyowetu thank you very much sir, so it was kind of a bluff question, because I tended to belive that only the elements from below the main diagonal get changed.

[@isaacamornorteyyowetu]

@@tudormarian4916 :) That's fine.

[@mathmatemathmade8985]

How did you choose x and y

[@isaacamornorteyyowetu]

x is always the pivot (diagonal) element and y is the element below the x value we want to change to zero. I trust the explanation helps.

[@joseantonioorozcotovar3426]

Isaac in 5:55 min, the slide show G2 wrong, check it

[@isaacamornorteyyowetu]

Thanks. You're right. It was a typographical error. Please, I will need you to subscribe to my channel.

[@nhattran5375]

do you have applications of givens rotation?

[@isaacamornorteyyowetu]

This approach is based on QR decomposition. It has it's application also in Neural Networks. Reference: "Application of the Givens Rotations in the Neural Network Learning Algorithm."

[@nhattran5375]

@@isaacamornorteyyowetu thank you so much

[@isaacamornorteyyowetu]

Welcome sir

[@francescofoschi8941]

Hello fellow tacticians

[@isaacamornorteyyowetu]

Hi Foschi

[@godvana1017]

Out of all the videos I have watched yours is the first one that really made me understand this rotation method for my upcoming exam. Really really well done, simple and straight to the point of how its done. Thank you so much and greetings from Germany!

[@isaacamornorteyyowetu]

Waow wow. Thanks. That's great to hear.