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Пікірлер
@pranavmahapatra 8 сағат бұрын
underrated as hell brother, this is so crystal clear, thank you for this
@rubyemes Күн бұрын
My main area of expertise is marketing analytics and I use linear algebra and eigen decomp for certain problems like identifying steady state market shares from a markov switching matrix. This is a brilliant video that gives me ideas for where I can push my models next.
@balrajsinghhanjra4899 Күн бұрын
How can we divide by a vector v, when we know that it is a vector , not a number
@MuPrimeMath Күн бұрын
We are not dividing by a vector. Instead we are dividing by v_i, which is one individual coordinate of a vector.
@ariyanariyan2001 2 күн бұрын
Thanks for your video?Would you please also explain the concept of fourier series and binomial theorem?
@guilhermefreitas6940 3 күн бұрын
aí pprt viado, tu é mt craque pqp
@samah6659 7 күн бұрын
thank you!!!
@john5635 9 күн бұрын
Thank you, great explanation
@BaymaxHiro-kh6my 10 күн бұрын
I also want a brain like yours for my engineering
@CharlesmuyobaMunenga 10 күн бұрын
I like the left hand writing 🎉❤🎉
@WD69420 10 күн бұрын
True sigma use u sub by u = xlnx-x ☝️🤓
@billycheung5114 11 күн бұрын
Bro it helps me a lot !!!!!
@ardatorer7025 12 күн бұрын
But wait this only applies to Aii and i is a not a any row but specific row that has largest magnitude. It is not arbitary. It is a choosen row
@MuPrimeMath 11 күн бұрын
You are correct. The index i is not arbitrary, but instead is the index of the largest entry of the eigenvector v with eigenvalue λ. Given a matrix, we don't know the eigenvector v, so we will not know the index i in general. The Gershgorin circle theorem simply states that the result holds for some i.
@rubyemes 12 күн бұрын
the missing piece for me! I knew it had to be a change of base problem
@reimannx33 13 күн бұрын
Better explained than most professors. Very well done - shows your clarity of understanding, clear and precise articulation, and a wonderful delivery style.
@ardatorer7025 13 күн бұрын
You sir a master mind at explaining things. It was very helpful.
@tsunningwah3471 16 күн бұрын
but how to generalize it into higher dimension? like 3x3 or even 10 by 10 determinant
@MuPrimeMath 16 күн бұрын
You could generalize the polar coordinate argument to N dimensions using N-dimensional spherical coordinates, although the algebra would get pretty messy! I'm not sure whether the complex numbers argument can generalize to arbitrary dimension because generalizations of complex numbers become weird past 8 dimensions (octonions are the last Euclidean Hurwitz algebra, which basically means that anything past that will be a little weird). You'd have to check the details.
@tsunningwah3471 16 күн бұрын
left handed mathematician. rare!😊
@mossy60661 19 күн бұрын
thank you so very much may god bless you
@osgwow 19 күн бұрын
0:40 How do you write dx in the denominator? Isn't that just a symbol to show that the derivative is being taken with respect to x?
@MuPrimeMath 19 күн бұрын
When I'm doing the limits, I'm using dx and dy as dummy variables. They are just the thing that's going to zero in the limit. It could have been any other letter instead, so dx doesn't have a special meaning there.
@bilalaitabbas7754 19 күн бұрын
thank you, Captain America,
@АлександрИванченко-х2р 20 күн бұрын
Прикольный прием, а так конечно интегр по parts
@cristiane.boghiu2941 20 күн бұрын
Elegant!
@cristiane.boghiu2941 20 күн бұрын
Very nice video!
@techwithdeepank 21 күн бұрын
You are good. I've watched like a dozen videos and couldn't get the clarity of what this (n m) thing is and I was just 30s in and you cleared it. Thanks bruh!
@MuzamilMehmood-sb7ok 23 күн бұрын
So cute 😊❤
@Ranid-eq6so 23 күн бұрын
The answer is: 152951/12375
@methatis3013 24 күн бұрын
If Im not mistaken, you didn't actually show that the tensor product of V and W is a vector space itself?
@MuPrimeMath 24 күн бұрын
The quotient of a vector space by a subspace is always a vector space. The big space Z is defined as a vector space consisting of a certain basis, and we quotient by the subspace generated by a certain set of elements, so the quotient is necessarily a vector space.
@methatis3013 24 күн бұрын
@MuPrimeMath right, this was skimmed over a bit, but it needs to be shown that a quotient of a vector space by a subspace is, again, a vector space. Although I do understand that would go beyond the scope of the video. I guess it's a good homework exercise
@the.lemon.linguist 24 күн бұрын
I understand that in the case of some curve r(t) that traces a curve, dr is a tiny change on r, and it can be found with r'(t)dr either by thinking of it (not very rigorously) as taking the dt from dr/dt and moving it over to the other side, effectively finding the "infinitesimal rise" by multiplying the derivative by an "infinitesimal run" or alternatively by thinking of it as converting a 0-form to a 1-form if you think of it in the nature of differential forms. In this case, would the analogy apply similarly with this? Would the partial derivative w.r.t. u times the differential du give that tiny change by similarly multiplying the rate by a tiny "run" of sorts?
@MuPrimeMath 24 күн бұрын
If the second variable v is held constant, then r(u,v) traces a curve in the variable u. Therefore the same reasoning applies as in the single-variable case as long as we assume that v doesn't change. So du times the partial derivative with respect to u gives a change in the curve along the u direction.
@the.lemon.linguist 24 күн бұрын
@ ohhh, i see! thank you so much!
@carlosaugustosarmentoferre376 25 күн бұрын
It is certainly fine to know Feynman's trick applied to integrals, he used it exactly as it stands, as a trick! One of his lemma was to shut up and calculate, simple that! But we must have in mind that in the end it might make sense, not just use it as a bypass. This is my message. The true knowledge is in calculus itself. I still use calculus as it was taught to me long time ago: u-substitution, integration by parts or partial fractions.
@shivamtiwaryslp8422 27 күн бұрын
3.3333.... is rational because we can write it as 30/9 but why pi isn't, well we can write it as 22/7 ???
@MuPrimeMath 27 күн бұрын
Pi does not equal 22/7; that is only an approximation. The first few digits of pi are 3.1415..., whereas the first few digits of 22/7 are 3.1428..., so they are not the same number.
@hocklintai3391 28 күн бұрын
Eureka!!!!
@facundo_5090 Ай бұрын
Lol i spent all yesterday looking for this, searching "proof of rotational formula", because the direct translation from spanish is rotational (rotacional) = curl. Thanks, i haven't seen the video but every video of yours has an amazing quality, you've helped me when solving a proofs book and now you're helping me on vector calculus!
@tunistick8044 Ай бұрын
2:30 is there an equivalence? or is it just an implication?
@MuPrimeMath Ай бұрын
If you're referring to the statement "xy is coprime to n if and only if x and y are both coprime to n", then yes, that is true. This is a consequence of Euclid's lemma, which states that if a prime p divides xy, then p must also divide at least one of x or y. Conversely, if p divides x or y, then clearly it also divides xy, since xy contains the prime factors of both x and y.
@loicboucher-dubuc4563 Ай бұрын
This is by far the best explanation on KZbin!
@nitinsharma9840 Ай бұрын
You just made it understandable ❤rather than memorising
@quercus_opuntia Ай бұрын
Hell yeah dude
@Jules23540 Ай бұрын
Very helpful, thanks
@mountaingreek747 Ай бұрын
Goat teacher
@gustafkugelberg3906 Ай бұрын
This is a great video, but I wonder, why do we first introduce Z as this massive vector space where the basis is every single pair of vectors in V and W, only to quotient away almost all of it? Couldn’t we just start with defining the space whose basis is all the pairs of BASIS vectors in V and W? Isn’t that what we end up with anyway?
@MuPrimeMath Ай бұрын
One of the key properties of the tensor product is the universal property. I explain the universal property and its applications in this video: kzbin.info/www/bejne/rIvdi5uagaiSj7M The universal property has to do with bilinear maps, and it turns out that the bilinearity properties are easy to check with the construction I use in this video. You could define the tensor product as you describe, using just a set of basis vectors from each space. However, this doesn't generalize well to modules, since a module doesn't always have a basis. The construction I use in the video works for modules as well.
@gustafkugelberg3906 Ай бұрын
@@MuPrimeMath OK thanks!
@BuddyNovinski Ай бұрын
I am annoyed that we never covered vector calculus in freshman year. We didn't have computer graphics back then, but it's no excuse.
@OisinDoyle Ай бұрын
it cannot be understated how underated this channel is. just been binging all of these over the break because I have to do these problems next semester and I feel so much more prepared. Thank you so much, I'm gonna show all my coursemates this channel now. Once again, thank sooooo much!!!
@aryandegr859 Ай бұрын
Game is game
@lennonpuls1878 Ай бұрын
Came here because I didn't know how Legendre was supposed to be pronounced. Can confidently say I never would've guessed it correctly
@eugenemars Ай бұрын
Hello, thank you for this great work. However, I ask myself a question. You say Z is a space vector. Could you be more accurate about its elements ? are they (v,w) ? could you define the addition law (u,v) + (r,s)= ? the external law c(u,v) = ? Thank you
@chanduyasodar6445 Ай бұрын
Videos are really good, they helped me to pass my undergrad end sem exams
@Wiik415 Ай бұрын
to be honest you're saving my life, thank you
@sugoplay Ай бұрын
Super! Thank you so much, Professor Mu! I’m a girl from Shanghai, and my name is Claire. I’ve also made some movies on my channel. Thank you again for helping me with this problem. I spent two days on it, trying lots of different ideas, but every time it felt like I was walking into a dark room and losing sight of my goal. I have to say that the "x mod a" approach is brilliant-it’s not just a clever idea, but a profound observation about the Cartesian product and remainders. I'm very excited to learn more marvelous ideas from you.😸
@anmolmishra4784 Ай бұрын
Amazing Thank you so much I do appreciate it ❤