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Matrix Factorization - Numberphile
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Күн бұрынFeaturing Professor David Eisenbud, director of the Mathematical Sciences Research Institute (MSRI).
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More videos with Professor Eisenbud: bit.ly/Eisenbud...
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The 17-gon: • The Amazing Heptadecag...
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@ianprado1488 4 жыл бұрын
Dr. Eisenbud seems like such a nice guy
@numberphile 4 жыл бұрын
He *is* a nice guy.
@andrewzhang8512 4 жыл бұрын
@@numberphile Why do you seem serious?
@MuffinsAPlenty 4 жыл бұрын
He absolutely is!
@vgstep 4 жыл бұрын
Totally
@shmunkyman33 4 жыл бұрын
"DR. EISENBUD IS INDEED A HUMAN WHO IS NICE" *blinks "HELP" in morse code*
@adamweishaupt3733 4 жыл бұрын
According to Google Scholar, "Homological algebra on a complete intersection, with an application to group representations" has 678 citations.
@andrewzhang8512 4 жыл бұрын
huh
@PHDnHorribleness 4 жыл бұрын
I feel like we should also be including papers that cite those 678 papers, and so forth, if we are using citations to measure impact.
@CommodoreHorrible 4 жыл бұрын
@@PHDnHorribleness "What is the cardinality of the set Q, where Q is the set of all papers that either cite "Homological algebra on a complete intersection, with an application to group representations" or cite a paper in set Q"
@samuelthecamel 4 жыл бұрын
@@CommodoreHorrible You should write a paper on it and then do the calculations on your own paper.
@martinpaddle 4 жыл бұрын
For a pure mathematics paper, that's a lot. In statistics, medicine, etc. you get different orders of magnitude, but there's less honesty in those numbers. In math, for example, you would typically only cite papers that are directly relevant to what you're doing (just as you would put authors in alphabetical order and don't include coauthors unless they contributed).
@davidr2421 4 жыл бұрын
It's pretty neat how he basically did "market research" on the physicists to see what paper they might like next, like the next version of a product. I've never thought about research fields interacting in that way.
@bonob0123 4 жыл бұрын
no i think it went the other way. He wrote the paper first and then the physicists found it useful and it became popular.
@Isiloron 4 жыл бұрын
@@bonob0123 David Vaughan was talking about the generalization paper, not the initial paper.
@marcoantonio7648 4 жыл бұрын
i know right?
@bonob0123 4 жыл бұрын
@@Isiloron Fair enough
@NYsummertimeCHI 4 жыл бұрын
@@Isiloron Thing is the physicists are usually like "I don't need the generalised version I just need enough to solve this specific problem." Then a hundred years later they come back with a "what were you saying about the n-dimensional generalisation again?"
@penisbreath952 4 жыл бұрын
love his answer at 15:01 "It makes me pleased, that's all really." :)
@randynguyen9006 4 жыл бұрын
@@ryanhenrydean1584 Thanks for pointing out his Username
@ebrahimsonday5941 4 жыл бұрын
"If you enlarge the domain of things you accept has a factorization then suddenly it becomes possible to factor." - Dr Eisenbud
@JonathanMandrake 2 жыл бұрын
To be fair, if you told a mathematician in the 16th century that x^2+y^2 factors into (x+iy)(x-iy) they would have told you 1. What are x,y, ^2 and i supposed to mean? We do math geometrically! 2. What square could have a negative area (regarding i)? Generalising is what always improved math, and if you see something that doesn't generalise itself but is revolutionary, it relies on at least a few new generalisations to work, or it should have been realised way sooner
@KilgoreTroutAsf 2 жыл бұрын
Yes, these are called field extensions.
@crimsonkhan3815 4 жыл бұрын
I love modesty of mathematicians..they do not brag about their works, because they have no idea where to use it, they just love mathematics, that's all for them.
@duartesilva7907 4 жыл бұрын
Yes. A mathematician knows he never knows everything.
@stv3qbhxjnmmqbw835 3 жыл бұрын
@@duartesilva7907 he also knows that he can't know everything. It makes him sad, but that's the reality.
@sb_dunk 4 жыл бұрын
12:23 "So the reason that x was ok here is because it was multiplied by..." "...zed" "...zee" "This interview is over"
@aceman0000099 4 жыл бұрын
We need a phoneticphile video to sort this out
@antagonistictherapy 4 жыл бұрын
@@aceman0000099 "phoneticphile" That's a weird way to spell Tom Scott.
@vae3716 4 жыл бұрын
It's zed actually
@stv3qbhxjnmmqbw835 3 жыл бұрын
@@vae3716 but more than 300 million people say it zee. So it's zee for US
@PeterBarnes2 2 жыл бұрын
I wonder, what do the rules say on whether or not that's a jinx?
@khalidbinwalid1566 4 жыл бұрын
Listening to him is so soothing. Also, I thought it’d be some familiar factorization from linear algebra, but it turned out to be much cooler!
@inyobill 4 жыл бұрын
And, Bam! Jus like hat, he day after my 72nd birthday, I learned something new. Thanks Dr. Eisenbud, Numberphile, and KZfaq.
@yorickdewid 4 жыл бұрын
We see David again!
@andrewzhang8512 4 жыл бұрын
yay
@neon-rust 4 жыл бұрын
If he ever wanted branch out, I can see him having a career in audio books with that buttery smooth delivery.
@neonblack211 4 жыл бұрын
Sometimes I think this guy is too high level for this channel. But I wanna see more from him definitely
@rogerkearns8094 4 жыл бұрын
Fair enough, but I find Dr Peyam's channel even more challenging sometimes.
@GruntDestroyarChannel 4 жыл бұрын
I guess it's better if you have some easy stuff and some hard stuff. Something for everyone.
@mobius32 4 жыл бұрын
I love Eisenbud's style! He has an ease of explanation that's very enjoyable to listen to.
@neonblack211 4 жыл бұрын
I’m not saying it’s not easy or enjoyable, take my comment with a grain of salt, just the fact he can explain topics like this without losing the layman without dumbing down the mathematics and the fact that he is actually a contributor to pushing mathematics is awesome, and it shows not only in his enthusiasm but his work
@neonblack211 4 жыл бұрын
I just mean that he is actually explaining topics on the cusp of his field, when a lot of these videos suffer from explaining things you would find in a typical course on various levels of mathematics, available on many other channels.... (not that that’s a bad thing either)... I meant it as a positive comment
@RaunySilva 4 жыл бұрын
Damn, I think it is just me missing numberphile's uploads frequently, but I was missing this guy. Such a nice person!
@romanbykov5922 4 жыл бұрын
You kinda lost me halfway to the end, but I still watched it through, cuz it's interesting.
@TakeWalker 4 жыл бұрын
You have my admiration, I was lost the moment he started talking about matrices. XD
@Carbon-XII 4 жыл бұрын
1:52 - "If you don't have enough tricks in your bag, put in a new trick" :-)
@Axacqk 4 жыл бұрын
Love how naturals are represented by a hammer (you can't hit a nail a time and a half), rationals by an an axe (used to "divide" firewood), and complex numbers by a compass (referring to geometric interpretation).
@stephenbeck7222 4 жыл бұрын
Enjoyed studying math and physics at Florida State University where Dirac spent his final years in semi-retirement (apparently he hated the humid summers compared to Cambridge but I bet the winters were much more enjoyable!). Many hours spent trying to understand analysis and algebra in the Dirac Science library.
@denisdaly1708 4 жыл бұрын
Glad for you Stephen. Sounds like you took alot in in your course. You have a connection to one of the main men of the 20th century.
@MuffinsAPlenty 4 жыл бұрын
12:59 "Proving this depends on the theory of finite free resolutions, in which I'm an expert." It feels like a bit of an understatement for Eisenbud to consider himself _only_ an expert on finite free resolutions :P
@Lastrevio 4 жыл бұрын
i read this comment as he said it
@alazrabed 4 жыл бұрын
Why would it be an understatement? I don't know much about Eisenbud's work.
@selenamertvykh6481 4 жыл бұрын
@@alazrabed Eisenbud literally wrote the book on commutative algebra.
@MuffinsAPlenty 3 жыл бұрын
@@alazrabed Sorry about the very late response! Eisenbud (and his collaborators, such as David Buchsbaum) proved some of the basic and foundational tools in studying finite free resolutions. He pretty much pioneered the topic!
@davidgillies620 4 жыл бұрын
In addition to factoring matrices, you can meaningfully take their logarithms, exponentiate them and take a matrix to the power of another matrix.
@typo691 4 жыл бұрын
Whaaaat? Really? How?
@lumer2b 4 жыл бұрын
@@typo691 Taylor series. Those functions (exponential, log) can be represented as an infinite sum. And we now how to sum matrices.
@tomkerruish2982 4 жыл бұрын
I question taking a matrix to the power of another matrix. Sure, you can do A^B = exp(B ln A), but you could also do A^B = exp((ln A) B), as there's no guarantee that ln A and B commute. (There's also no guarantee that ln A exists - it doesn't, in general - but we can assume it does for the purposes of a definition.) I must admit, the concept is new to me, and quite interesting. Thank you.
@prikarsartam 3 жыл бұрын
Such a great interaction with a very humble mathematician. It really is nice!
@Cobalt0000000 3 жыл бұрын
I was just procrastinating on a commutative algebra assignment and stumbled upon this video, not realizing this is the very David Eisenbud from the commutative book I was reading! (The book is great, of course.)
@danielurbinatoro9496 4 жыл бұрын
A gem per se (and especially in these troubled times). What a pleasure to watch Prof. Eisenbud. Thank you!
@ubertoaster99 4 жыл бұрын
This is mindboggling stuff. Kudos to Paul Dirac who only lived a mile or two down the road from where I am now!
@DyllonStejGaming 4 жыл бұрын
I just got done with my Linear Algebra course, and you *had* to remind me of it just a few days later :P
@yrrgallerte354 4 жыл бұрын
Isn't it always nice to see that the stuff you learned is usefull? :)
@FtwXXgigady 4 жыл бұрын
Oh wow it's the TAs guy
@victorarturoibanezaliaga8783 4 жыл бұрын
bro u should watch linear algebra on 3b1b channel if you haven't
@jledragon 4 жыл бұрын
Same, I just finished a Bayesian Machine Learning course yesterday and thought I had seen my last matrix for a while!
@brightsideofmaths 4 жыл бұрын
No one is ever really finished with Linear Algebra :)
@alaanasr7505 4 жыл бұрын
Early Numberphile videos talks about a specific number. Nowadays Numberphile videos talks about partial derivatives and matrices. . . . . Future Numberphile videos talks about hypertopology and combinatorial number theoy.
@narutosaga12 4 жыл бұрын
So very true!
@aleksapetrovic7088 4 жыл бұрын
I don't mind 😊
@recoveryemail1046 4 жыл бұрын
Honestly, I don't even have a clue what they are talking about
@yigitsezer6696 4 жыл бұрын
i hope
@jamirimaj6880 4 жыл бұрын
Numberphile in 2020s
@mathhack8647 2 жыл бұрын
It's not about mathématics only, Everybody listening here can appreciate , modesty, humbleness, altruism, soul beauty and a lot of hope for next scientist generations. thanks for those precious minutes of pure pleasure.
@charlieangkor8649 3 жыл бұрын
This number domain expansion technique is especially useful during exams. Example: a kid gets an exam problem: divide 173 by 7. So the kid writes: "Let's extend the set of integers by a new number i, so that 7i=173. So the result of our problems is i". And this way he avoids the mentally exhausting process of actually solving the problem.
@pkmath12345 4 жыл бұрын
Wow great! Def my favorite in linear algebra~ like the way you present it~
@andrewxc1335 4 жыл бұрын
"So citations are like your video views, then?" More like "engagement statistics," since it only counts those people who have actually used your work to do further work.
@shaileshrana7165 4 жыл бұрын
I understood nothing but I loved listening to him.
@roderickwhitehead 4 жыл бұрын
True fact... saw thumbnail of David in my sub feed and was all like, "Aw hail, yeah!"... my favorite guest on Numberphile... and makes me wish I could have had him for a professor.
@exxzxxe 8 ай бұрын
Every school in the World should have a David Eisenbud teaching math!
@ImKurono 4 жыл бұрын
He did the matrices portion very well. I enjoyed this alot and it makes me miss learning math. Thank you for this. He seems to be a very humble person.
@nataliaquinones4356 4 жыл бұрын
I really enjoy hearing Dr. Eisenbud! :) Thanks for taking the time to make such wonderful videos.
@nightworg 4 жыл бұрын
That was awesome. I really like David Eisenbud explanation, and that was an interesting conversation about his work.
@lambda494 4 жыл бұрын
The inspiration from Dirac is really awesome. That guy was a genius. A random comment from him inspired Feynman's approach to quantum mechanics. And I use matrix factorizations at work all the time. This is wonderful.
@sarahcogswell9166 Жыл бұрын
Dr. Eisenbud makes this content so approachable
@flymypg 4 жыл бұрын
Oh, I would have dearly loved to see a step-by-step worked example of this! Perhaps for a trivial-but-real case that illustrates the basic mechanism in a way that may fail to illustrate its depth, but still shows its utility. Perhaps in a follow-up video?
@michelebotticelli3258 4 жыл бұрын
I Just love listening to Professor Eisenbud: he is crystal clear and surprisingly relaxing for me.
@NeoLogicification 4 жыл бұрын
Could someone explain the connection between finding the root of xy-uv and finding roots of x^2+y^2+z^2+t^2? I don't see how it relates to complex numbers.
@martinepstein9826 4 жыл бұрын
Let's say the first equation is rs - uv. We get the second equation if we set r = x + iy s = x - iy u = z + it v = -z + it
@Miyelsh 4 жыл бұрын
@@martinepstein9826 To get the equation with -t^2, set u = -z + t and v = z + t
@cretinobambino 4 жыл бұрын
I too felt like this was an important link that was missing.
@kaakatin 4 жыл бұрын
Could you make a video about Clifford algebra? It is a pretty cool way to simplify and unify a lot of mathematics in physics, and I think it deserves to be shown to larger audiences. Dirac's matrix problem in this video is basically Clifford algebra, but just with a matrix representation.
@javierantoniosilva8477 4 жыл бұрын
I'd love to see more of Numberphile regulars explaining us part of their research.
@CosmiaNebula 4 жыл бұрын
Another perspective on Dirac's equation is that it is factored using numbers from Clifford Algebra (a vast generalization of complex numbers, quaternions, and such).
@thatdude_93 4 жыл бұрын
Yesterday I was rewatching all of Professor Eisenbuds material on this channel and was hoping that there'll be more soon. Looks like my wish came true
@paulpantea9521 4 жыл бұрын
We all need more Eisenbud in our lives.
@gabrielhermesson9926 4 жыл бұрын
As soon as they mentioned Dirac in the context of the mathematical toolbox, I thought they might talk about the Dirac delta.
@DerNesor 4 жыл бұрын
This channel is 86% reason why I will quit my job and go for a PHD ... I can't live without this stuff ^^
@1978Maedhros 4 жыл бұрын
OMG that's Eisenbud?? The writer of one of my favorite books! ❤️❤️❤️❤️❤️❤️❤️❤️
@johnchesterfield9726 4 жыл бұрын
Would you mind telling me what book it is?
@chunchen3450 4 жыл бұрын
Amazing! Never realized that a polynomial can be directly linked to matrix. Usually it is taught as a series of equations. It would be interesting to know any applications that prefer to turn matrix into ploynomials
@Belioyt 4 жыл бұрын
He just talked about Dirac and how he applied it to quantum mechanics
@Belioyt 4 жыл бұрын
It's also used in string theory
@tomkerruish2982 4 жыл бұрын
For square matrices, there's the characteristic polynomial, whose (ordinary numerical, i.e. complex) roots are the eigenvalues of the matrix. Interestingly, the matrix itself is a root of its characteristic polynomial.
@WaffleAbuser 4 жыл бұрын
7:57 I want him to add the parentheses so badly!!!!! This is torture!!!!
@moodleblitz 4 жыл бұрын
Why?
@worldOFfans 4 жыл бұрын
@@moodleblitz becaus xy-uv * A =/= (xy - uv) * A
@brightsideofmaths 4 жыл бұрын
I feel with you :)
@MuffinsAPlenty 4 жыл бұрын
@@worldOFfans But xy-(uv*A) doesn't really make any sense at all, so there's only one reasonable interpretation of xy-uv * A.
@ericbischoff9444 4 жыл бұрын
@@MuffinsAPlenty you're right, but you should not rely on reader doing the correctness work for you ;-) .
@samuelthecamel 4 жыл бұрын
Prof. Eisenbud: "Matrices" High School Students: ight, imma head out
@englishmotherfucker1058 4 жыл бұрын
ight imma still in
@mananself 4 жыл бұрын
“Dirac was satisfied. He invented matrix mechanics...” but I thought matrix mechanics was developed by Heisenberg.
@Rififi50 4 жыл бұрын
He misspoke, I guess. What he shows in the video leads to the Dirac equation, a relativistic wave equation and not matrix mechanics. He is after all, as he says himself, not a physicist ;) The whole motivation Dirac had was that the original relativistic wave equation, the Klein-Gordon equation, yields wave functions that cannot be transformed into probabilities. Taking the square root of it, so to say, would solve the issues but without considering matrix factorization there is just no way. Matrix mechanics, from looking through Wikipedia, appears to be the early version if the Heisenberg picture. A refrence frame where you evolve operators instead of wave functions. With fixed wavefunctions, the formalism can be considered as working only with matrices (given a chosen basis).
@mananself 4 жыл бұрын
Rififi50 yeah I was waiting for him to say Dirac introduced antimatter to interpret the solutions of the Dirac equation.
@MatthijsvanDuin 4 жыл бұрын
To be fair, he's not a physicist
@tombulous 4 жыл бұрын
I'm introducing operator algebra (and factorization) to my Quantum Mechanics Students this week. I'm showing them this video because I find a nice introduction to the idea before we dive into some mathematics. Nice video.
@bittertea 4 жыл бұрын
I aspire to be at his level of chill.
@digitig 4 жыл бұрын
I loved "Nature just said, 'you should have been using matrices all along'"
@davidianmusic4869 4 жыл бұрын
Mind, phew, blown. Yes, you’ve reached this audience, thanks for the enlightenment.
@user-my5qk5xu1d 4 жыл бұрын
Just been into trouble with Unitary Matrix Decomposition for weeks and Now I see this in my recommendation......
@wierdalien1 4 жыл бұрын
Any use?
@user-my5qk5xu1d 4 жыл бұрын
@@wierdalien1 No
@TheTwick 4 жыл бұрын
I could listen to prof Eisenbud for hours. Thank you.
@allmycircuits8850 4 жыл бұрын
I'm currently working on rendezvous algorithm which uses quaternions to represent rotation of one object relative to other.But for initial "guess" there is affine approximation: we convert image of object into 2x2 matrix and 2x1 vector. And one of my tasks was to factor this 2x2 matrix into rotation, scale and "aspect" (looking from the side). So this video was very close to me: matrix factorization and also Dirac trick which has something to do with quaternions, though I still don't understand this connection thoroughly...
@manueldelrio7147 4 жыл бұрын
I am really fond of Doctor Eisenbud's videos, and by proxy, of himself!
@thescienceprint5825 4 жыл бұрын
David Eisenbud is an American mathematician. He is a professor of mathematics at the University of California, Berkeley and was Director of the Mathematical Sciences Research Institute from 1997 to 2007. He was reappointed to this office in 2013, and his term has been extended until July 31, 2022.
@user-sq5hv9tj3i 4 жыл бұрын
Respect to Eisenbud, and his gigantic GTM Commutative Algebra
@selenamertvykh6481 4 жыл бұрын
@@edawgroe It's a graduate-level text. At minimum you'd need to have had an undergrad abstract algebra course that tackled rings and fields.
@thederivationchannel4243 4 жыл бұрын
What a brilliant educator. So humble and down to earth
@danibarack552 4 жыл бұрын
I would have liked to see him actually factorize the polynomial hr started with..
@mufasao6776 3 жыл бұрын
"If you want to solve an equation like 3x-1=0, you can't solve that in integers, so you invent rational numbers (fractions), and then you suddenly can solve it; x is 1/3. Or, if you said 3x+1=0, then you'd have to know about negative numbers too. And for a while, negative numbers were sort of very strange things in mathematics. Then they got ordinary, and we're happy to use them." "Nature somehow follows along, or, really, nature was ahead of us there, I think. So nature knew about complex numbers, but didn't bother to tell us for a long time. And then we needed them for something, and we realized that they were useful, and now are the basis of lots of physics and everything. So they're really out there in nature, even though they're called imaginary or complex."
@SuperCuteAnimeWaifu 4 жыл бұрын
Thanks you. Really kinda clicked the relation between the SU(2) generating matrices and pauli's matrices.
@senkottuvelan 4 жыл бұрын
Even if I couldn't understand at first. He made me understand like magic. Great video from a nice guy. 😊
@daniellanes813 4 жыл бұрын
Started watching, watching took over, this Dr. got some chill charisma.
@thescienceprint5825 4 жыл бұрын
Paul Adrien Maurice Dirac was an English theoretical physicist who is regarded as one of the most significant physicists of the 20th century. Dirac made fundamental contributions to the early development of both quantum mechanics and quantum electrodynamics.
@bittertea 4 жыл бұрын
Could we have more linear algebra on this channel please?
@ericpowell96 4 жыл бұрын
He has such a relaxing voice 😴
@Belioyt 4 жыл бұрын
Yes, I want him to narrate an audiobook
@zozzy4630 4 жыл бұрын
I like that now we know how to find the square root of a matrix, but he still never explained how xy-uv is actually the same as -c^2(d^2/[dt^2]) + (d^2/[dx^2]) + (d^2/[dy^2]) + (d^2/[dz^2]). I'm sure it's something he's taking for granted that linear algebra students already know, but now I'm just confused and lost. Can we get a video about that sometime?
@ycu4AB 4 жыл бұрын
i don't know the analogy of the differential operator to the polynomial t^2+x^2+y^2+z^2. but this polynomial can be factored into matrices, because it is degree 2 (as he later explains). the xy-uv stuff is only an interlude to motivate matrix factorization. there is no relation to the t^2+x^2+y^2+z^2 polynomial.
@nicolasboyardi9382 4 жыл бұрын
Maybe it has something to do with changing the basis, but is just a quick thought I got.
@zozzy4630 4 жыл бұрын
@@ycu4AB Oh, thank you! That was the main thing that had me stuck; I didn't realize he was using it as an analogy. I suppose xy-uv is probably the simplest multi-term polynomial of all terms with degree greater than 1, and proving that that works is enough to prove that the 4D quantum equation works, too. I'm still a bit lost on that first step as well, but I think with enough time and pencil and paper I could probably figure it out - my intuition tells me you probably have to integrate it and then re-derivate it a few times and eventually a factor of 1 pops out of one of the terms or something.
@vs-cw1wc 4 жыл бұрын
It's called lightcone coordinates and has applications in string theory. look that up.
@matiasreinoso3393 4 жыл бұрын
This is one of the best videos on this channel thus far
@redambersoul 4 жыл бұрын
He is just the guy I want to take classes om algebra ... He is heartwarming in his wise love to the area he is an expert of.
@dominiquelaurain6427 4 жыл бұрын
Thanks Professor Eisenbud, I learned more about maths and physics history. You gave more than the maths ideas but also the fighting spirit to go farther :-)
@Ricocossa1 4 жыл бұрын
I remember doing that little computation in particle physics. I didn't realise it was such an important mathematical concept.
@evenprime1658 3 жыл бұрын
okay i see my mans coming up with more quadratic formulas
@skylardeslypere9909 2 жыл бұрын
I've got a question about his theorem. If you do allow the matrix factorization to include constants, does it mean we CAN factor any and every polynomial? Take P(X,Y) = X+Y² for example. If we 'treat' it as another polynomial P(X,Y,Z)=XZ+Y², factor that one without constants, and plug in Z=1, do we not get a factorization?
@meexi9824 4 жыл бұрын
I don’t get it , I almost watch every Numberphile Video on release , but this video didn’t show up in my feed. Might be the best video on yt I’ve seen in weeks. May the algorithm be with you for the next video . Love the Eisenbud Videos and hoping for another one with Clifford Stoll
@abhinavagarwal244 4 жыл бұрын
Fantastic....always had this question in mind...nobody answered this way
@trevorteolis3691 4 жыл бұрын
Great video, Professor Eisenbud is great to watch. I would've liked to see more details though.
@sbmathsyt5306 4 жыл бұрын
Such a soothing voice and very interesting video as per usual.
@guangruli4486 3 жыл бұрын
He actually has a book Commutative algebra: with a view toward algebraic geometry being cited >8000 times
@jaserogers997 3 жыл бұрын
Wow, what a nice dude! I kind of want to just sit on his knee. "Doctor Eisenbud, tell me the one about matrix factorisation and the three bears".
@cwaddle 4 жыл бұрын
So what is the application of the matrix factorization? The traditional polynomial factorization will tell you where the zeros are, but does the matrix factorization do the same thing?
@kiro9291 4 жыл бұрын
this professor is a lovely teacher
@foxtrot.tango.whisky 4 жыл бұрын
Can we get a video on probing variation of the fine-structure constant using the strong gravitational lensing? Please. Thank you.
@braedenlarson9122 4 жыл бұрын
I’m actually writing my essay on paraxial matrices in optics! Matrices are super convenient for simplifying complicated systems!
@Squirtledrool 2 жыл бұрын
i really like the theorem, also i like how he sounds like mr. burns
@andrewsterrett9834 3 жыл бұрын
Wikipedia says David Eisenbud is the son of Leonard Eisenbud who was a doctoral student of Eugene Wigner who was the brother of Margit (Manci) Wigner who was married to Paul Dirac
@mehfak 4 жыл бұрын
I really love Professor Eisenbud videos. I would have loved to have him teach me mathematics (especially algebra). Is there any course from him online ? (PDF, Vidéos, etc.)
@user-sq5hv9tj3i 4 жыл бұрын
you can just buy his GTM, the thickest GTM of all
@alicewyan 4 жыл бұрын
@@user-sq5hv9tj3i Lee's Smooth Manifolds is thicker IIRC
@Belioyt 4 жыл бұрын
@@user-sq5hv9tj3i what's GTM?
@MuffinsAPlenty 4 жыл бұрын
@@Belioyt Graduate Texts in Mathematics. Prof. Eisenbud's "Commutative Algebra: with a View Toward Algebraic Geometry" is about 800 pages long.
@boywithacoin 7 ай бұрын
i thought he was going to discuss traditional QR factorization methods, like QR or LU decomposition. however, his discussion mainly focused on factorizing polynomials, which required the use of matrices. surprisingly, this method didn't lose its informational integrity during the process. i have a feeling OP chose a generic title for the video for better SEO but perhaps should re-name it appropriately.
@MrYashraj 4 жыл бұрын
A Person With Exceptional Skill In A Particular Area❤❤❤.
@lamgam-ts8tr 4 ай бұрын
Dr. Eisenbud is a treasure
@mattbell888 4 жыл бұрын
Couldn’t you just substitute a new variable x = y^2 any time you have a linear term? Could you apply this to things of a non-positive integer order, like x^y, or x^4.87 or x^-2?
@kcmichaelm 4 жыл бұрын
This entire video was so heartwarming. I loved it.
@RalphDratman 4 жыл бұрын
This is unusually clear! Well, to my slow brain it is unusual to be able to follow along so easily. So, thank you.
@alfeberlin 4 жыл бұрын
"Why is it your most cited paper?" -- "Well, I didn't write anything else interesting ..." 😉😄
@nagoshi01 4 жыл бұрын
At 8:48, how does multiplying two 2x2 matrices line up with a 4x4 matrix? The matrix squared should stay 2x2 and diagonal, with squared elements only.
@MuffinsAPlenty 4 жыл бұрын
They aren't 2x2 matrices he's multiplying together. Those are "block matrices". Remember that A and B are both 2x2 matrices.
@omarsamraxyz 4 жыл бұрын
I love Dr. Eisenbud❤️❤️