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this is actually a ray plane intersection!

many thanks from Kurdistan your explanation is perfect professor. I had a question according to my calculation and running the algorithm on computer, in the matrix H2H1A the last element should be -9/5 at 41:12 am i correct?

Thanks for the video, it's very good. (*˘︶˘*).。.:*♡ I'm watching from Russia, I don't know the language well, but this video still helped me. I still couldn't solve my task, but in any case I'll think about it some more. However, I have a question: could there be any problems in the solution due to the fact that, for example, we count with an accuracy of 5 or more decimal places? If not, then I'm in despair, I can't do the calculations and I don't understand why yet. P.s.1: Sorry for my bad English, anyway thank you again for the video. With it I passed at least the theoretical exam.ヾ(@^▽^@)ノ P.s.2: Maybe in 10 years someone will look at this and help me with the calculations, it would be funny. I'll be old already, and someone will send me the solution to these equations or something like that. I'm attaching my example here just in case. All the numbers here are separated by tabs, I don't know if TH-cam saves it, but you can paste the matrix into a notepad. We need to solve this matrix B = (A | b) using the Givens method (rotations) 0.94241 -9.92593 -4.90992 -4.10518 8.62312 110.64248 3.95281 -9.73429 9.62224 2.55386 8.13700 198.54478 3.94003 -6.60744 8.03506 -6.22550 4.25786 202.69444 4.40064 9.45029 7.78432 -4.23471 3.47524 92.84404 9.89481 -5.46737 8.68865 -5.27678 0.31915 165.27806 I calculate the rotation matrix G1 0.09452 0.99552 0 0 0 -0.99552 0.09452 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 Then I multiply G1 by the matrix B 4.02418 -10.62888 9.11505 2.1544 8.9156 208.11323 -0.56457 8.96138 5.79742 4.32818 -7.81538 -91.38035 3.94003 -6.60744 8.03506 -6.2255 4.25786 202.69444 4.40064 9.45029 7.78432 -4.23471 3.47524 92.84404 9.89481 -5.46737 8.68865 -5.27678 0.31915 165.27806 The first element of the 2nd row should be 0, but I have -0.56457 There is a mistake here somewhere, but I don't know where. Basically, the only thing I don't understand is why I can't get 0 here. Or maybe I didn't watch the video carefully. You need to solve this option manually, so the option with writing code will not work here.

Awesome explanation!

Thank you so much Professor! Wonderful series!

Thank you for the wonderful videos, professor! They have been a huge help for my NLA class.

nou joe aur eej ferrie choet tietcher! tenk joe ferrie meutch!!

give examples to explain the topic. You're just reading the slides. Didn't understand a single thing. Same shit is written in my notes, but how do I actually implement it?

Still helping students in 2024, here from Romania, keep up with these kind of videos!

This is insanely good

Hi sir, could you give me any link for the scientific computation course which discusses about advanced linear system solvers? Thank you.

You're always apologizing for the proofs, but they're the best part!

Very clear explanation. This is good stuff. I have 2 questions: 1) Why does Ai stay upper Hessenberg? 2) I don't really grasp why the diagonal elements of Ai converge to the eigenvalues? Thanks for the video!

Reduction interval [a;b] to the [-1;1] interval can be done by substitution but the biggest problem with Gauss-Legendre quadratures is calculation of nodes I would like to see comparison between Gauss-Chebyshev quadratures Chebyshev nodes are easy to compute while Legendre nodes needs numerical methods (I can get coefficients of Legendre polynomial of degree n in linear time from power series solution of differential equation but to calculate nodes I need numerical methods such as QR method for eigenvalues)

Could we use deflation as well to compute the eigenvalues ?

Great content Professor

You've become my professor of linear algebra. Thank you very much.

Super. Thanks.

you explain everything in an extremely clear manner, thanks a lot

Hi Sir this video is exceptional it summarizes all of SVD. I have just a one question can we find AA^T first which will give U matrix and then funding V matrix using relation U(sigma) = AV, i mean the reverse process of what is usually found in books

Thanks! What do you mean by "power of matrices property"?

Great video. Where do you explain the power of matrices property?

how to choose sigmas when shifting not knowing the eig values

Hi. I am Chong Li from Bloodsport. Love your lectures sir!

Wow!

Thank you, dear sir. Very simple and easy to understand. I was a math undergrad, and I am going back for my master's after 10 years, so this is a huge help for revision.

This has been a perfect explanation about the householder's QR decomposition! Really grateful for your video!!

please, can you send me a link to find the gradient(derivative) of norms? thank you

Thank you. Extremely helpful!

Greatly help with my understanding in concepts and algorithms!!

this is so great! Thank's

Wonderful lecture. Missing such mathematics for a long time. Thanks!

i really like your videos but can you explain how to get H2 and H1 simply

Each video of these series is great, thanks from the bottoms of my heart,

Hi Prof Martijn, I always review your videos for Numerical Linear algebra, your explanation is just make sense and intuitive. Thank you.

Hello professor, may I know which book you have taken for reference, thank you 😊

Watching from Zürich, this is so great! You should have more subscribers

you are a bless Dr Martijn. Deep appreciation for your videos, you are a great lecturer

I absolutely loved your explanation for choosing the sign at 23:25, I couldn't find anywhere else on the internet whether we are supposed to use +, - or signum and why, thank you a lot professor.

Excellent explanation!

σ is the smallest singular value of A∗A, µi are the singular values of A, and we have used the fact that A∗A is normal. Why norm of (A*A)^-1=(norm A^+)^2 Can you explain for me ? Thank you so much

I've seen these videos and frankly they are some of the best on the web, in terms of clarity and information. Love it.

Check Video 2-3 in this series. It discusses sensitivity of linear systems

Can you help me explain sensitivity of variable A

One important thing : Cross product is a vector Americans misuse the terms cross product and its length For example in Convex hull they use term cross product no matter that cross product works only for 3D vectors and they have the length of cross product of their mind

Thank you so much for these lectures ❤

can you provide code for this

Dear Professor, thank you very much for the explanation! How could I deal with complex matrices? Can I use QR/Schur for the complex case? As soon as I understood, you derived the explanation for the real values.

And suppose I would like to get some orthogonal polynomials via orthogonalisation How Householder transformation would help ? I know how to use modified Gram-Schmidt for this purpose We have inner product than v_{j}^{T}v_{k} For example inner product for Chebyshov (sh is hard and over that e there are two dots which Russians usually dont write so it is better to write o here) polynomial is sum(a_{2k}*1/(2^(2k)*binomial(2k,k),k=0..floor((m+n)/2)) where p(x)q(x) = sum(a_{k}*x^k,k=0..m+n) so this inner product is different from that produced by v_{j}^{T}v_{k}

well done appreciate your effort