This explanation with red and blue spaces is so good. It takes usually a whole year of studying to reach this level of intuition, and this video does it all in 10 minutes. Thanks for making the effort!
@Kumurajiva
Жыл бұрын
This is why pure math is simpler than physics, or applied math.
@gulamm1
5 ай бұрын
Pure math may be simpler but how it is applied to understand physical phenomena is more important.
@Phi1618033
6 ай бұрын
Finally, a proper explanation in plain English. Been trying to wrap my head around this for over a year now.
@timurgabdyshev1139
6 ай бұрын
why?
@TunaBear64
3 ай бұрын
@@timurgabdyshev1139Let's just say that people don't joke about the definition of a tensor being "a tensor" for no reason.
@spiderjerusalem4009
22 күн бұрын
@@timurgabdyshev1139most of the time, it was defined without any motivation
@davidgoldgruber8541
Жыл бұрын
Best and most compact explanation/visualization of the Cauchy stress tensor I have seen so far. Wish this video had existed a few years ago when I studied the topic at uni.
@not2tired
6 ай бұрын
Studying stress tensors at unicycle!
@sethhhhhhhhhhhhhhh
Жыл бұрын
This is a wonderful introduction!! This past semester, I took linear algebra and differential equations. Tensors were hiding in the background, as boogeymen that our teacher warned us we would come across later. Your visualizations were both beautiful and clear. Excited for the rest of the series!! :)
@bencrossley647
Жыл бұрын
Worth sharing with your lecturer. They often appreciate a good resource!
@juniorcyans2988
Жыл бұрын
Oh I’m gonna take differential equations this coming semester and linear algebra next semester. This is the first video I watched in 2023! I was wondering where I would encounter tensor, then you leaked a hint😂
@bobbwc7011
Жыл бұрын
Tensors are like John Wick ...it's not just the boogeyman, it's the thing you sent to kill the fucking boogeyman. Also, this is a very "accessible" introduction via physics and engineering. I've had a mathematician as professor when I took tensor calculus as a university-level engineering scientist. An absolute nightmare because the first half of the semester was pure mathematics, tensorproduct, tensor bundles, blargh, and only after a Guantanamo-level of torture - when you had gone blind from all the superscript and subscript indexes - the "practical" stuff started to show itself on the horizon. That class "Tensorrechnung and Tensoranalysis für Ingenieure" / "tensor algebra and tensor calculus for engineers" was my happiest 3.0 ("satisfactory", C) ever and I was the third best in class with that result LOL (such results used to be normality at German universities in the old pre-Bologna system). Sometimes mathematicians are simply evil people. :D
@-danR
Жыл бұрын
This video is the natural second step after Dan (no relation) Fleisch's video introduction to tensors.
@timothyjohnson1511
9 ай бұрын
Thank you for presenting in dark mode, easy on the eyes. Looking for dark mode presentations of electrodynamics with dipole radiation, and accelerating charge.
@jamierbb
Жыл бұрын
Time to get smart on a Thursday morning.
@Neerzzz
Жыл бұрын
Here its 21:32
@bryanb2653
Жыл бұрын
Big learn
@corrompido7680
Жыл бұрын
why of course the first coment I see in a completely random maths-physics video is one with homestuck pfp sure why not
@Aecor
Жыл бұрын
Friday baby
@justanotherguy469
Жыл бұрын
2:10 a.m. Fri. morning. Lovin it!
@scene2much
Жыл бұрын
I've been trying to get a PERFECT understanding of Tensors for decades.... this was Wonderful!
@dialectphilosophy
Жыл бұрын
Most intuitive and simple explanation of a tensor you can come across on KZitem!
@visualchallenge2413
Жыл бұрын
It is amazing what you can learn in 12 minutes ! I have no use for this information but I watched this video in order to get rid of the mystification about this subject that bothered me for more than 30 years. Thank you for this great effort of explanation.
@mikip3242
Жыл бұрын
Finally!!! Someone in KZitem decides to make the concepto of Tensor easier and meaningful to mortals.
@justanotherguy469
Жыл бұрын
You know, I was just thinking the same thing, but then it dawned on me that most mortals do not even know what a scalar is.
@anjanavabiswas8835
9 ай бұрын
@@justanotherguy469 Fair enough.
@rantorakoto8785
Жыл бұрын
From the bottom of my heart, thank you 😭❤️ you simply did an amazing work. I've been unsuccessfully trying to understand this for 3 years, I eventually dropped out and just moved forward using tensors without having any idea of what it really is, but now, thanks to you, after 11 minutes, It's finally clear to me, so thank you very much.
as an engineering student those 12 minutes here have more blessing than a 4 month course of my engineering program in university. Just Perfect
@yevgeniygorbachev5152
Жыл бұрын
I'm working through the Eigenchris series right now, and I'm really excited to see other math/physics youtubers take a crack at it.
@cykkm
Жыл бұрын
Eigenchris' lectures are amazing! He disposes with a few common conventions, both in notation (simply AB instead of common A⊗B); and, especially important, coordinate conventions (he doesn't normalize the unit in the direction of θ by 1/r), which makes their action the same as that of partial derivative. They _are_ PD's! The first time I saw that, I thought, wowzers, why do the most textbooks manage to kill this correspondence, so natural? First by tearing the 1/r out of the object, then sticky-taping it to it, because from now on you're bound to carry them together. And they don't mean anything anymore...
@justanotherguy469
Жыл бұрын
He is amazing and very detailed.
@Oxygenationatom
5 ай бұрын
?
@あい-w2o5m
6 ай бұрын
This is the world's easiest explanation of tensors. I wanted to see it when I was a college student over 30 years ago.
@AlexBesogonov
Жыл бұрын
This is the best introduction I've seen! People typically try to introduce tensors from the other direction, from the abstract side, and only at the end moving to matrix representation.
@adamb7088
Жыл бұрын
OMG!! I do believe I now know how important it is to calculate the Eigenvalues and Eigenvectors of a tensor field. Thanks.
@christopherneufelt8971
Жыл бұрын
Did you have enough? Are you happy? Finished? I am ready to have tears in my eyes, this is probably the best description of a complicated subject that I ever seen. Really beautifully made with clarity and insight. Bravo, bravo.
@sumairahmad9464
Жыл бұрын
Freaking amazing bro. Much appreciated. Can't thank you enough for taking the time out to make this for us!
@justanotherguy469
Жыл бұрын
RIGHT?!!!
@laurenwrubleski7204
Жыл бұрын
I've been looking for a good explanation of tensors for years! I'm so excited for the rest of this series!!
@pianojay5146
Жыл бұрын
came for tensor, staying for stunning visuals for material mechanics! great job!
@gabitheancient7664
Жыл бұрын
you have no idea how good I feel seeing the springs moving with that specific sound, pls never abandon this sound, I need it together with springs, springs are so much cooler with this sound added
@adrian_sp6def
Жыл бұрын
The shortest and best vid aboud tensors! I really love short and compact videos like this. I do not have enough time on my life to watch >10min videos. In this video there is only knowledge without unnecessery staff around. BIG THANKS!
@joejoejoe3
Жыл бұрын
At the end of my Calc III course a few weeks back I randomly stumped upon the idea of a tensor (namely trying to figure out if ∇𝐅 was meaningful,) so this couldn't have come out a better time. Definitely going to keep up with the series!
@eqwerewrqwerqre
Жыл бұрын
Pleaaasseee pleaaasssee post more of this series. There's such a lack of intelligible introductions to tensors on the internet. I've seen eigenchris's videos too and I think this is the best possible addition to his work as it approaches from an entirely different angle (visualization) and is extremely valuable to me. I would be eager to see why EM tensors are antisymmetric or really any continuation of this series, this was a great video. I've subscribed in the hopes of more
@t3db0t97
8 ай бұрын
Of all the videos I have watched on tensors, this is the first time I've *actually* understood them. Outstanding work!
@DrDeuteron
10 ай бұрын
Great video for engineers. If you move beyond vector a arrows, and say, replace “Z” with cosine theta, then vectors are the things that can be rotated amongst themselves, and require a 360 degree rotation to remain unchanged. There are 3 of them. Rank 2 tensors are such things that require 180 deg. There are five of them. Rank 3 require 120 degrees, there are 7 of them. Keep going, and you have the spherical harmonics, which are a great way to visualize tensors, since you can draw them. Btw: the reason we even care about vectors and tensors is exactly these property under rotation, and ps: there are things that require 720 degrees of rotation to be unchanged. Hint: there are 2 of them.
@IAmNotARobotPinkySwear
9 ай бұрын
This is like discovering the holy grail of explanation videos. Saved, and I'm gonna download an offline copy just in case. Thank you so much, subscribed.
@ThreeEarRabbit
Жыл бұрын
Did the name tensor come from "tense" or "tension", as in their application in stress analysis? Just curious...
@adrienconverset6571
Жыл бұрын
Using them tenses your brain, the name stuck. (That was a joke, don't quote me)
@estranhokonsta
Жыл бұрын
A quick search gives me: "Tensor" comes from the Latin "tendere", which means "to stretch/pull (out)" To note that "tension" also comes from the Latin "tendere". So they are definitively related, just not directly.
@justanotherguy469
Жыл бұрын
Great video. It elevates my understanding of tensors to the level of intuition. Love your graphical presentation.
@evancarpenter
Жыл бұрын
Holy smokes, this is the explanation that’s making it click for me After years of hearing how it’s a map and invariant and all the other things, seeing the relationship between the two spaces and exploring the relationship between the components helps a lot, incredible video!
@tim40gabby25
Жыл бұрын
Hi. As a complete curious amateur, this was perfectly clear. Well done.
@justanotherguy469
Жыл бұрын
That is how you know a teacher knows his stuff.
@tedsheridan8725
Жыл бұрын
Very cool video. Even after taking two classes involving tensors (years ago), I never fully got them. This was very easy to understand naturally.
@dank3k
Жыл бұрын
This is beyond cool. Please continue with the series!
@robocop30301
Жыл бұрын
This is the greatest video that was ever made.
@michaelblankenau6598
Жыл бұрын
Very well explained . Making clear what the geniuses have always understood .
@avocado1998
Жыл бұрын
Best video I've ever watched. So clearly explained and the 3D visualisation is incredibly helpful when you're trying to learn this stuff. It's so hard to learn this just on paper in 2D without animations.
@MCSteve_
Жыл бұрын
I imagine you can find the the new coordinate system with no apparent matrix sheering by figuring out the eigenvectors. Also with that anti-symmetric matrix, I imagine it has the property of no divergence yet has curl, which satisfies the property of electromagnetic fields (according to Maxwell's equations). I just don't understand what makes this connection of symmetry and zero divergence. Amazing video, I think I finally understand the idea of tensors.
@DavidPumpernickel
3 ай бұрын
Beautiful video, especially in showing the construction of a tensor space as the product of vector spaces
@DevRajyaguru-lx8pi
Жыл бұрын
Best explanation of the tensors I found After years, Thank you so much!
@IoldxmanI
Жыл бұрын
This is the best explanation I have come across. Please release the second part.
@jeremiahvanhook1114
Жыл бұрын
Visualization is such a key component of understanding all mathematical concepts. Part 2 PaRt 2 PART 2!!!!
@patrick1532
Жыл бұрын
4:24 Ugh, dude, I had to figure this out for myself when I took a mechanical design course in school. Prof just jumped straight into doing problems without explaining anything about what she was doing. Glad my understanding of it has been validated though.
@kimchi_taco
Жыл бұрын
holy cow. I realized I didn't understand tensor in my Physics degree. Brilliant work! Thanks!
@LucyHealthy97
Жыл бұрын
You have a beautiful brain! I feel so excited to watch your video. Please post visualization of tensors - part 2. I'm waiting for it
@khajiit92
Жыл бұрын
always struggled with understanding tensors and this is the first one that's making it click, thanks so much!
@fitness60plus52
Жыл бұрын
you know what? this is the first video ever (among zillions) that made me grasp what a tensor is about. 👍👌
@timothywelk3244
8 ай бұрын
This is incredible. I wish I had your KZitem page when I was in college.
@ProkofievAMD
Жыл бұрын
WOW ! after all these years I finally understand what a tensor is ! 😲 great video. Thanks from France 🇫🇷
@webgpu
Жыл бұрын
sorry for my ignorance, but are these tensor more related to physics or AI, or it's indifferent?
@udiprod
Жыл бұрын
They are more related to physics and math. AI uses a simplified version of this term, basically meaning a multi-dimensional array of numbers.
@billvvoods
Жыл бұрын
Awesome visuals and explanations. This is the video I’ve been waiting for all my life. Thanks for producing this.
@Ammar2b
Жыл бұрын
that's one of the greatest videos on KZitem for mechanical engineers! Thank you
@sanjaythorat
4 күн бұрын
Very simple and powerful explanation. Keep making more videos.
@rudypieplenbosch6752
Жыл бұрын
This is very interesting, especially seeing electromagnetism as a tensor.
@enricolucarelli816
Жыл бұрын
Superb. This is the kind of videos that expand my mind. 👏👏👏👏👏
@ale8088
Жыл бұрын
Wow! Thanks a lot for this valuable content Sir! "2 vector spaces" related together by a correspondence between "label", the weighted raw combination of the matrix to obtain the vector that acts on a particular inclined slice (matrix product: namely a linear transformation) and the example of the sphere, where every direction in the first space have a realted direction in the second space, make finally reasonable understand why, in abstract math, tensors are defined directly like linear map between dual spaces. Whith only a table of 9 number (6 due to simmetry of this pshysic problem) it is possible to manage any slice no matter its orientation. Obvious: only if we assume hypothesis of linearity is true (and locally it is). If we think about this, it results amazing how mr Cauchy, a great Franch engeneer, in middle of 1800, realized all those ideas without linear algebra, rather founding linear algebra itself and matrix calculus.
@Rodrigoviverosa
6 ай бұрын
FINALLY I understand Tensors, after 10 years of gratuation and all day watching ton of videos on YT haha, thanks!!!
@gparizoto
Жыл бұрын
Beautiful physical interpretation of tensors, keep doing this great job!
@luisdiamonv
Жыл бұрын
Thanks you, I was traying to understand this concept, your explanation help a lot, thanks again.
@kalpitkatpara2720
Жыл бұрын
My mind is completely blown by your explanation!!! amazing work! you are a real gem to humanity! 💕✌✌👍👍
@thomaschiesa8202
Жыл бұрын
This deserves a standing ovation, a masterfully excellent video!!!
@marcfruchtman9473
Жыл бұрын
Incredible visualization. Thank you for making this video.
@alexandreboulch5455
7 ай бұрын
Best video on the stress tensor I’ve seen so far. Thanks!
@alfahad7433
Жыл бұрын
awesome! awesome! awesome! For the first time I understood the topic a bit. Please continue the series as I believe that there are a huge number of students feeling like me...🙏🙏🙏
@Songvbm
Жыл бұрын
Definitely a valuable video tutorial for me. My request to the uploader is to provide the visualization of "tensors applied in the domain of Statistics & ML", if possible. Thank you.
@davidjones5319
Жыл бұрын
Excellent. Best intro to the concept of tensors I’ve seen. Very helpful
@petersimon985
4 ай бұрын
Hi, Thank you for making this great effort. Unselfish and straightforward video. ❤
@vanderkarl3927
Жыл бұрын
I don't know why I wasn't subscribed before considering I watched and enjoyed all the halting problem and Bell Inequalities related videos!
@Edu888777
Жыл бұрын
Really good vídeo, one of the best! Very didactic. Thank You !
@rockstonic52
Жыл бұрын
cant right now honey, new udiprod about math i dont need to know
@jimparsons6803
3 ай бұрын
Interesting and thanks. A lot of folks think that math, generally speaking is a human invention, entirely, which would apply to vector spaces. A belief system, been on the US' PBS a couple of times. The takeaway (one that I came to back in the day) is that math is a descriptive language.
@Kart-sl2qq
Жыл бұрын
This video was just sensational, thank you
@reup6943
Жыл бұрын
Am I wrong thinking the statement "stress tensor are always symmetrical" strictly speaking is wrong? In order to simplify the topic the video states the cube should always be in equilibrium, so I assume the video only discuss the case where our material does not move or deform (state of static equilibrium), in this precise case the stress tensor must be symmetrical (and stress force will respect Newton's 3rd law). However it may be the case that at some point in time the material moves or deforms right? Does this mean that the stress tensor is not symmetric anymore?
@colafish2152
Жыл бұрын
Amazing video, it give a vivid visual explanation to some very abstract mathematics-physics concept. Actually, I spend lot's of time to study these concept by myself, but I still can't fully understand these concept, what I learn from this video it worth then these book i read.
@apoorvmishra6992
Жыл бұрын
Eagerly waiting for part 2 buddy....
@StefanosZormpas
10 ай бұрын
the Chinese say "a picture, a thousand words" and I say "a video of yours, five years of university". My congratulations, keep up the excellent work
@EMLtheViewer
Жыл бұрын
I cannot stress enough how much this video helped me. (pun unintended, but welcome) Just reading about tensors was not enough, and I always wondered what exactly made them different from matrices. Thanks for this explanation!
@Ganerrr
Жыл бұрын
i rlly like this style of video, keep it up!
@zacknstuff1611
5 ай бұрын
This is the best video about tensors
@Wilhelm8e
Ай бұрын
9:44, I am a bit confused. All the vectors has only x component, so they should all stack on the X-axis. Is this correct?
@udiprod
Ай бұрын
See at 5:50 and 6:40. On the sphere at position (x,y,z) there's red vector which is a weighted sum of the matrix rows: x*row1+y*row2+z*row3. In our case all the rows are zero except row1 which is (1,0,0) So on position (x,y,z) on the sphere we draw a red vector (x,0,0)
@Wilhelm8e
Ай бұрын
@@udiprod Thank you for the explanation! Really informative videos. I have reproduced the stress tensor field based on your video.
@sudonim7552
Жыл бұрын
As an engineering major who has seen this math in many structures classes, but it's always been presented as simply a matrix representation of a system of linear equations. I've never realized that I was using tensors before.
@KalebPeters99
Жыл бұрын
This is such a remarkable introduction. Bravo 👏👏👏
@danielobambelo1411
Жыл бұрын
Yes, finally new video, havent even seen it but i know that it will be great, also those who say first are stupid.
@tf2excession
Жыл бұрын
This is an incredible video, I see so many people have struggles with tensors & change of basis. If you can bring in some intuition for the universal property as well, this will be the single canonical series to explain them
@gomdangdang
Жыл бұрын
You are amazing. I heard that tensor is the object which does not depend on change of coordinate. Now it is somehow clear to me, but I am really looking forward to the next video. Thank you!!
@mics1417
Жыл бұрын
Wow! This is probably the best demo and explanation that I've seen on YT. I wish that tensors and its application in maxwell's equations could have been covered in undergrad EE rather than basing our knowledge on using the derived formulas. Should I have went for physics instead, or do all undergrad programs ignore tensors?
@thomasriishojgaard5677
Жыл бұрын
Goated video, inertia tensors and euler angles were throwing me off a little in my mechanics class but this video saved me
@Midazc
11 ай бұрын
Such a clean, concise explanation and visualization. Well done!
@bassamxp
Жыл бұрын
This is totally magnificent ... thank you. I'll make sure my students follow this video and the channel
@thevelar7139
Жыл бұрын
No way no way no way , can i cry just bcuz i understand it ,daamnnn you did exellent explanation man ❤❤❤❤❤❤❤
@kh4y3m
Жыл бұрын
Awesome! Every time I'll teach linear algebra I'll make sure everyone see this video!
@najahsaeed2006
11 ай бұрын
Thank you so much for the great effort in this video, all the best, and keep it up
@markhuebner7580
9 ай бұрын
Very quick and very insightful thank you!
@safaahamdan5668
7 ай бұрын
This video is most credible great fantastic representation of tensor ❤❤❤
@casenc
Жыл бұрын
I can't wait for part 2!
@maximpavlov5379
Жыл бұрын
A very intersting and comprehensive explanation!
@joserodrigomorenolopez6651
Жыл бұрын
Excelent video, makes visual everything that needs to be visualized. Congrats
@luismiguelmurogarcia7431
5 ай бұрын
What a fantastic video, it has helped me a lot, thank you
@megri3441
Жыл бұрын
Thank you for this excellent demonstration. I'm able to imagine how machine learning models learn from the data. It was looking like a magical mystrious for me.
@natan4238
5 ай бұрын
this video is how i know my university meche department has no clue how to teach. in 12 minutes this video explains away most of the gaps from stress analysis because instead of using tensor math we just goofed off with random simplified equations
@prabinpradhananga9031
Жыл бұрын
This is terrific! The most lucid visualization of tensors I have ever seen! Just a question, which software/code did you use to create the visualization for tensors?
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