Further Matrix Decompositions: LU, Cholesky, QR, and SVD

Рет қаралды 12,909

Күн бұрын

Пікірлер: 79

@cgifrog Ай бұрын

Would love to see more math videos. Maybe differential equations, graph theory, discrete mathematics, or even some analysis would be amazing but perhaps out of scope. Your Linear Algebra and Calculus videos carried me last semester, thanks for all that you do!

@ProfessorDaveExplains Ай бұрын

Diffeq is coming soon

@haavensiye250 28 күн бұрын

@@ProfessorDaveExplains THE GOAT. IS. BACKKKKKKKKKKKKK!!!!! (bro came just as i was starting lin alg 😭🙏)

@merlinssearch 20 күн бұрын

Yea same

@Pragmatic-Physicist 15 күн бұрын

@@ProfessorDaveExplains I cannot express how happy I am that you are working on diff eq.

@viculty4724 12 күн бұрын

@@ProfessorDaveExplains WWWWWW

@HypervioletGeometryDash Ай бұрын

FINALLY we're getting more maths videos!!!

@maheshmanani2991 Ай бұрын

Exactly dude

@tristancools Ай бұрын

I was yesterday just rewatching the whole linear algebra series, its like a gift to get this new linear algebra video

@FishSticker Ай бұрын

Let's see the flat earthers debunk this one

@null_s3t Ай бұрын

*try to

@benvel3392 Ай бұрын

"No one has seen a matrix in real life, you dumb sheeple 😤😅🤣"

@luthfil2728 Ай бұрын

It's simple really. Dave forgot to include the angles of incidence when solving for the fractal matrix. This is because he use the cartesian method which is all sorts of angular momentum wrong. Also the sun gave birth to the earth and some alien race called Annunaki put us here for some reason. Yes I am an avid viewer of Billy Carson and Terrence Howard. How did you know?

@MrWompz 21 күн бұрын

@@luthfil2728😂😂

@MOSMASTERING Ай бұрын

One of my favourite quotes about science actually came from Ricky Gervais.. He said - "If all science was wiped out, it would still be true, and someone would rediscover it. If you wiped out religion, it would never come back in the same form."" Facts are facts, truth is truth - and as we slowly learn more, we get closer to it. The laws, constants, rules and fundamental constituents of reality will always be the same. In addition to physics, biology would be rediscovered from scratch to be the same as well. Nobody would stop at intelligent design. As soon as we discovered DNA it was game over for ID, all the clues are there written into it.

@gabor6259 Ай бұрын

If science and religion were wiped out at the same time, then I have a suspicion that religion would come back in roughly the same shape. Because human psychology.

@GuapoTaco21 Ай бұрын

Just in time for winter break now that I’m done with linear algebra

@akshatmisra767 Ай бұрын

lol same

@void0669 Ай бұрын

thanks professor dave, this will help me find eigenvectors for my wave conjugation homework

@Joel-The-Bad Ай бұрын

Dave did you see the final experiment Antarctica flat earth destruction video? I know you were talking about it at one point. It happened. Lmao

@pwd-tk9 Ай бұрын

This video is underrated. Most of this stuff is relevant to learning ML stuff.

@godofmath1039 Ай бұрын

This one sparks joy...

@Blingsss Ай бұрын

Amazing video! Matrix decompositions are fascinating tools for simplifying complex linear algebra problems. I’ve always found LU and QR decomposition particularly helpful in solving systems of equations, while SVD opened my eyes to its importance in data science and PCA. SolutionInn has been a lifesaver for breaking down these topics with clear examples and resources. It’s amazing how these techniques connect to so many applications from optimizing algorithms to understanding transformations. Definitely worth diving deeper into.

@absence9443 18 күн бұрын

This was actually really helpful

@backyard282 Ай бұрын

I'm a math undergraduate and we didn't learn this in Linear Algebra. Thanks dave

@lksr2095 Ай бұрын

Thank you so much dave! I was waiting for more math videos! You are the best!!

@obbeel Ай бұрын

That looks useful. Thank you for the video.

@majyaz 24 күн бұрын

i want through this playlist. THANK YOU

@undine8750 Ай бұрын

If, for some matrix A, you compute A = QR using QR decomposition, and then set A to RQ, and repeat many many times, legend has it that eventually A has its original eigenvalues listed on its diagonal.

@AutumnWheel5446 Ай бұрын

You have a gift for teaching, have you considered making a series about computer science?

@fingler Ай бұрын

Hi Dave! Love to see the math content! I don't comment very much, but I just wanted to reach out to tell you about this awful anti-mainstream "math" channel called "New Calculus" that I stumbled upon. The shit this guy spews in his videos is pretty ridiculous, but some of the highlights are: "Infinity isn't real" and "The square root of 2 isn't a number". I commented under a few of his videos correcting his obvious mistakes and misunderstandings, and he responded with a temper tantrum video of him saying how badly he wanted to find me and beat me up, which promptly got taken down. I would love to see a debunking of his bullshit, but I also worry that giving him any kind of attention would only grow his audience. Anyways, keep up the good work!

@s1nd3rr0z3 Ай бұрын

Mathematics returns! Bitterly ironic for me as I was hoping to take linalg next semester but it wasn't offered and I'll have to wait until next fall :(.

@LordCaptainFather Ай бұрын

MSc Dave teaches math, and teaches it well...

@carrizzle9586 Ай бұрын

I took Finite Mathematics (Matrix algebra and probability) before I joined the engineering program and then took Linear Algebra and I didn't know that algebra could get that difficult. A lot of rules that relate to vectors in space.🤯

@SEGAClownboss Ай бұрын

The math messiah has returned!!!!!

@TwoCraZyEyes0 Ай бұрын

Dave when are you doing a video about the final experiment?

@ash-lo2dc Ай бұрын

you are a hero

@ticonderogafutterman3111 Ай бұрын

Also Jordan decomposition and Schur decomposition might be mentioned here... (if possible)

@hurithinkbefore1340 Ай бұрын

Did you know Will from TFE is a young earth creationist? Of course you did. Respect for science and cudos from Austria.

@jessicatymczak5852 Ай бұрын

So, how would you get the density matrix, sum^n_i phi_i * phi_i n

@Masteralien186 Ай бұрын

MR FARINA show me how a cell decomposes into eigenvectors. CLUELESS

@leeyoheem Ай бұрын

Hey Dave, can you do a video reviewing the data on binaural beat effectiveness? As well as brown/white/pink noise? And by effective, I mean increasing focus/productivity, making someone less distracted - that sort of thing. At least to me it seems very hard to reach any conclusion whether these things are effective by reading the data, yet a lot of people do recommend them. I'd be interested to know if at the end of the day it's more of a placebo/conditioning effect or a somewhat effective tool

@SianNadine Ай бұрын

I forgot all this but as soon as you started talking I thought I was back in my uni lectures miss doing matrices for fun

@GregWike 16 күн бұрын

If you don’t mind me asking, do you ever plan on covering PDE’s or are you only going to do ODE’s?

@ProfessorDaveExplains 16 күн бұрын

Both

@davidmurphy563 Ай бұрын

Oh, I literally just finished coding an LU decomposition method as part of my matrix inverse! What are the chances?! ``` def lu_decomposition(self): n = self.shape[0] L = Matrix.generate_zero(size=n).components U = Matrix.generate_zero(size=n).components for i in range(n): for j in range(i, n): U[i][j] = self.components[i][j] - sum(L[i][k] * U[k][j] for k in range(i)) for j in range(i, n): if i == j: L[i][i] = 1 else: if not U[i][i]: raise ValueError("Matrix is singular, no inverse exists.") L[j][i] = (self.components[j][i] - sum(L[j][k] * U[k][i] for k in range(i))) / U[i][i] return L, U ```

@jambogamer-je2nf Ай бұрын

im a non coding person. can you explain what this is?

@davidmurphy563 Ай бұрын

@@jambogamer-je2nf Oh, it's just part of a matrix datatype I made which outputs two matrices based on the object's matrix; the lower and upper triangular decompositions. I then use these elsewhere to return the inv matrix. The code instantiates two n x n zero matrices and then I loop to factorise the given square matrix into the product of the matrices by looping the rows and components. I run a check to see if the determinant is zero, that's just to check that it has full rank / all the basis vectors are linearly independent. It's all a bit verbose as it's generating two matrices simultaneously. In the video it was done by Gaussian elimination. I did the determinant calc that way but it's painful to code as there are three distinct operations but I believe it's also O^3. My code only is only defined on square matrices though.

@AlgisBogomol Ай бұрын

Are category theory videos coming soon?

@fframemrl Ай бұрын

hey professor dave, have you ever heard about mnemonics? i think it is perfect for making a new series, i would be very happy to explain everything i know, it is basically a memory hack that you have probably heard, and some people teach it very bad and it gives bad perception to ones who have learned, i will discuss abiut loci method, dominick's system(pao) combined with major system, used by many top level memory athlethes

@spideybot Ай бұрын

Could you please make a seperate video on QR method please?

@pmsoltan Ай бұрын

For the Cholesky decomposition you need to assume that A is not only hermitian, but also positive (some people call this "positive definite"). Also the introduction to the SVD is way off - the problem is not in A having "repeated eigenvalues" (you mean its eigenvalues have non-trivial multiplicities), but the decomposition itself is presented correctly.

@user-ph2jf4ji1j 26 күн бұрын

I immediately noticed that too. I like that Dave is doing these videos but I don't think he has a deep intuitive grasp of this topic and is mostly just reading from a textbook. SVD should be discussed in context of linear transformations and elliptical forms, and projections.

@sheldonwoolman5602 Ай бұрын

You're a good man Dave

@hanifarroisimukhlis5989 Ай бұрын

Brushing up my matrix knowledge

@AbhiramN_1289 Ай бұрын

I just finished up my Linear Algebra course this semester. I passed, but the timing is hallarious.

@Debra-ly9yt Ай бұрын

Hey P. Dave, how bout a debate with ARCHAIX. Talk about EPIC!

@NexusBanks Ай бұрын

I can’t wait for Dave to address the final experiment, and all the insanity flat earthers claim about it, especially Eric Dubay.

@cadenbanke7544 Ай бұрын

Hey Professor Dave, I was just watching your video from 3 years ago talking about quantum mystics and there was a video that sounded eerily similar to what terrence howard says. then it hit me. they are the exact same talking points except that terrence doesn’t talk about crystals. You should compare what he says to that original video because it’s word for word and you debunked him 3 years ago before he was even popular for this crap 😂😂

@chandra9466 Ай бұрын

Professor Dave could you create a video of how UV, AAS, GC and any spectrophotometry please 🙏

@theshape3988 Ай бұрын

I truly want to learn this stuff but it to dumb to interpret this stuff lol thank you though for showing it

@Ctrl-Z-Renders Ай бұрын

LINEAR ALGEBRAAAA

@mew-zm2oz Ай бұрын

@isitme1234 Ай бұрын

MIsterrrrr Farrrrrrina!!!!!

@picklerick.n.666 Ай бұрын

Merry Christmas(the mass of Christ) ❤❤❤

@NullSpectralZenithCipherVoid Ай бұрын

Sir can you please make videos on these chapters (before 15 january) 👇👇👇👇 1. Sets 2. Relations and Functions 3. Trigonometric Functions 4. Principle of Mathematical Induction 5. Complex Numbers and Quadratic Equations 6. Linear Inequalities 7. Permutations and Combinations 8. Binomial Theorem 9. Sequences and Series 10. Straight Lines 11. Conic Sections 12. Introduction to Three-Dimensional Geometry 13. Limits and Derivatives 14. Mathematical Reasoning 15. Statistics 16. Probability 17.Relations and Functions 18. Inverse Trigonometric Functions 19. Matrices 20. Determinants 21. Continuity and Differentiability 22.Applications of Derivatives 23. Integrals 24. Applications of the Integrals 25. Differential Equations 26. Vector Algebra 27. Three-Dimensional Geometry 28. Linear Programming

@murcje Ай бұрын

I never watch these super difficult videos. I'm just here to upvote anyway because I love what you do! 🤍

@joem6908 Ай бұрын

My brain hurts 😫

@plashplash-fg6hd 23 күн бұрын

There are 69 comments. LoL, Nice, 70 now, anyway, is this talking about a Fractal Matrix? It's talking about shapes in matrices which leads me to believe that Billy Carson was right about a "fractal matrix".