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Visualization of tensors - part 1 

udiprod
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This video visualizes tensors. It shows some introduction to tensor theory and demonstrates it with the Cauchy stress tensor.
Future parts of this series will show more theory and more examples.
It talks about the term 'tensor' as used in physics and math. In the field of AI the term 'tensor' was borrowed with a simplified meaning. In AI it simply means a multi-dimensional array. So for example the array "double a[4][6]" (4 by 6 matrix of doubles) is called a second-order tensor, but there's no special relationship to vector spaces, as shown in the video.

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26 сен 2024

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Комментарии : 543   
@jamierbb
@jamierbb Год назад
Time to get smart on a Thursday morning.
@Neerzzz
@Neerzzz Год назад
Here its 21:32
@bryanb2653
@bryanb2653 Год назад
Big learn
@corrompido7680
@corrompido7680 Год назад
why of course the first coment I see in a completely random maths-physics video is one with homestuck pfp sure why not
@Aecor
@Aecor Год назад
Friday baby
@justanotherguy469
@justanotherguy469 Год назад
2:10 a.m. Fri. morning. Lovin it!
@Phi1618033
@Phi1618033 7 месяцев назад
Finally, a proper explanation in plain English. Been trying to wrap my head around this for over a year now.
@timurgabdyshev1139
@timurgabdyshev1139 7 месяцев назад
why?
@TunaBear64
@TunaBear64 3 месяца назад
​@@timurgabdyshev1139Let's just say that people don't joke about the definition of a tensor being "a tensor" for no reason.
@spiderjerusalem4009
@spiderjerusalem4009 25 дней назад
​@@timurgabdyshev1139most of the time, it was defined without any motivation
@davidgoldgruber8541
@davidgoldgruber8541 Год назад
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
@not2tired 6 месяцев назад
Studying stress tensors at unicycle!
@sethhhhhhhhhhhhhhh
@sethhhhhhhhhhhhhhh Год назад
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
@bencrossley647 Год назад
Worth sharing with your lecturer. They often appreciate a good resource!
@juniorcyans2988
@juniorcyans2988 Год назад
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
@bobbwc7011 Год назад
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
@-danR Год назад
This video is the natural second step after Dan (no relation) Fleisch's video introduction to tensors.
@timothyjohnson1511
@timothyjohnson1511 9 месяцев назад
Thank you for presenting in dark mode, easy on the eyes. Looking for dark mode presentations of electrodynamics with dipole radiation, and accelerating charge.
@scene2much
@scene2much Год назад
I've been trying to get a PERFECT understanding of Tensors for decades.... this was Wonderful!
@yousefamar288
@yousefamar288 Год назад
as an engineering student those 12 minutes here have more blessing than a 4 month course of my engineering program in university. Just Perfect
@あい-w2o5m
@あい-w2o5m 7 месяцев назад
This is the world's easiest explanation of tensors. I wanted to see it when I was a college student over 30 years ago.
@dialectphilosophy
@dialectphilosophy Год назад
Most intuitive and simple explanation of a tensor you can come across on RU-vid!
@visualchallenge2413
@visualchallenge2413 Год назад
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.
@christopherneufelt8971
@christopherneufelt8971 Год назад
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.
@AlexBesogonov
@AlexBesogonov Год назад
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.
@pianojay5146
@pianojay5146 Год назад
came for tensor, staying for stunning visuals for material mechanics! great job!
@HitAndMissLab
@HitAndMissLab Год назад
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
@Kumurajiva Год назад
This is why pure math is simpler than physics, or applied math.
@gulamm1
@gulamm1 5 месяцев назад
Pure math may be simpler but how it is applied to understand physical phenomena is more important.
@sumairahmad9464
@sumairahmad9464 Год назад
Freaking amazing bro. Much appreciated. Can't thank you enough for taking the time out to make this for us!
@justanotherguy469
@justanotherguy469 Год назад
RIGHT?!!!
@gabitheancient7664
@gabitheancient7664 Год назад
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
@adamb7088
@adamb7088 Год назад
OMG!! I do believe I now know how important it is to calculate the Eigenvalues and Eigenvectors of a tensor field. Thanks.
@t3db0t97
@t3db0t97 8 месяцев назад
Of all the videos I have watched on tensors, this is the first time I've *actually* understood them. Outstanding work!
@laurenwrubleski7204
@laurenwrubleski7204 Год назад
I've been looking for a good explanation of tensors for years! I'm so excited for the rest of this series!!
@IAmNotARobotPinkySwear
@IAmNotARobotPinkySwear 9 месяцев назад
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.
@adrian_sp6def
@adrian_sp6def Год назад
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!
@tim40gabby25
@tim40gabby25 Год назад
Hi. As a complete curious amateur, this was perfectly clear. Well done.
@justanotherguy469
@justanotherguy469 Год назад
That is how you know a teacher knows his stuff.
@eqwerewrqwerqre
@eqwerewrqwerqre Год назад
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
@joejoejoe3
@joejoejoe3 Год назад
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!
@kimchi_taco
@kimchi_taco Год назад
holy cow. I realized I didn't understand tensor in my Physics degree. Brilliant work! Thanks!
@evancarpenter
@evancarpenter Год назад
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!
@justanotherguy469
@justanotherguy469 Год назад
Great video. It elevates my understanding of tensors to the level of intuition. Love your graphical presentation.
@dank3k
@dank3k Год назад
This is beyond cool. Please continue with the series!
@DrDeuteron
@DrDeuteron 10 месяцев назад
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.
@tedsheridan8725
@tedsheridan8725 Год назад
Very cool video. Even after taking two classes involving tensors (years ago), I never fully got them. This was very easy to understand naturally.
@robocop30301
@robocop30301 Год назад
This is the greatest video that was ever made.
@LucyHealthy97
@LucyHealthy97 Год назад
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
@timothywelk3244
@timothywelk3244 8 месяцев назад
This is incredible. I wish I had your RU-vid page when I was in college.
@fitness60plus52
@fitness60plus52 Год назад
you know what? this is the first video ever (among zillions) that made me grasp what a tensor is about. 👍👌
@rudypieplenbosch6752
@rudypieplenbosch6752 Год назад
This is very interesting, especially seeing electromagnetism as a tensor.
@DavidPumpernickel
@DavidPumpernickel 3 месяца назад
Beautiful video, especially in showing the construction of a tensor space as the product of vector spaces
@StefanosZormpas
@StefanosZormpas 10 месяцев назад
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
@michaelblankenau6598
@michaelblankenau6598 Год назад
Very well explained . Making clear what the geniuses have always understood .
@patrick1532
@patrick1532 Год назад
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.
@vanderkarl3927
@vanderkarl3927 Год назад
I don't know why I wasn't subscribed before considering I watched and enjoyed all the halting problem and Bell Inequalities related videos!
@enricolucarelli816
@enricolucarelli816 Год назад
Superb. This is the kind of videos that expand my mind. 👏👏👏👏👏
@apoorvmishra6992
@apoorvmishra6992 Год назад
Eagerly waiting for part 2 buddy....
@marcfruchtman9473
@marcfruchtman9473 Год назад
Incredible visualization. Thank you for making this video.
@gparizoto
@gparizoto Год назад
Beautiful physical interpretation of tensors, keep doing this great job!
@IoldxmanI
@IoldxmanI Год назад
This is the best explanation I have come across. Please release the second part.
@sanjaythorat
@sanjaythorat 7 дней назад
Very simple and powerful explanation. Keep making more videos.
@billvvoods
@billvvoods Год назад
Awesome visuals and explanations. This is the video I’ve been waiting for all my life. Thanks for producing this.
@DevRajyaguru-lx8pi
@DevRajyaguru-lx8pi Год назад
Best explanation of the tensors I found After years, Thank you so much!
@alexandreboulch5455
@alexandreboulch5455 7 месяцев назад
Best video on the stress tensor I’ve seen so far. Thanks!
@thomaschiesa8202
@thomaschiesa8202 Год назад
This deserves a standing ovation, a masterfully excellent video!!!
@avocado1998
@avocado1998 Год назад
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_
@MCSteve_ Год назад
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.
@khajiit92
@khajiit92 Год назад
always struggled with understanding tensors and this is the first one that's making it click, thanks so much!
@Ammar2b
@Ammar2b Год назад
that's one of the greatest videos on RU-vid for mechanical engineers! Thank you
@alfahad7433
@alfahad7433 Год назад
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...🙏🙏🙏
@kalpitkatpara2720
@kalpitkatpara2720 Год назад
My mind is completely blown by your explanation!!! amazing work! you are a real gem to humanity! 💕✌✌👍👍
@davidjones5319
@davidjones5319 Год назад
Excellent. Best intro to the concept of tensors I’ve seen. Very helpful
@jeremiahvanhook1114
@jeremiahvanhook1114 Год назад
Visualization is such a key component of understanding all mathematical concepts. Part 2 PaRt 2 PART 2!!!!
@sudonim7552
@sudonim7552 Год назад
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.
@ProkofievAMD
@ProkofievAMD Год назад
WOW ! after all these years I finally understand what a tensor is ! 😲 great video. Thanks from France 🇫🇷
@Kart-sl2qq
@Kart-sl2qq Год назад
This video was just sensational, thank you
@casenc
@casenc Год назад
I can't wait for part 2!
@Songvbm
@Songvbm Год назад
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.
@rktiwa
@rktiwa 7 месяцев назад
Missed it by as many as 50 years!
@petersimon985
@petersimon985 4 месяца назад
Hi, Thank you for making this great effort. Unselfish and straightforward video. ❤
@Edu888777
@Edu888777 Год назад
Really good vídeo, one of the best! Very didactic. Thank You !
@KalebPeters99
@KalebPeters99 Год назад
This is such a remarkable introduction. Bravo 👏👏👏
@luisdiamonv
@luisdiamonv Год назад
Thanks you, I was traying to understand this concept, your explanation help a lot, thanks again.
@zacknstuff1611
@zacknstuff1611 5 месяцев назад
This is the best video about tensors
@rockstonic52
@rockstonic52 Год назад
cant right now honey, new udiprod about math i dont need to know
@DERIVATIVES-mh6ej
@DERIVATIVES-mh6ej Год назад
So a tensor field is like if you took many different vector fields, folded each of them onto themselves until they each became tiny individual points, and used those points to make up a new, higher order field. It's like a field with each point individually corresponding to its own entire vector field. Just wow.🤯
@maximpavlov5379
@maximpavlov5379 Год назад
A very intersting and comprehensive explanation!
@robibezerra
@robibezerra Год назад
Really good introduction!!!
@chej9
@chej9 Год назад
Wait what. That electromagnetic fields part is THE best cliffhanger ive seen in a while.
@kh4y3m
@kh4y3m Год назад
Awesome! Every time I'll teach linear algebra I'll make sure everyone see this video!
@Midazc
@Midazc 11 месяцев назад
Such a clean, concise explanation and visualization. Well done!
@colafish2152
@colafish2152 Год назад
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.
@thomasriishojgaard5677
@thomasriishojgaard5677 Год назад
Goated video, inertia tensors and euler angles were throwing me off a little in my mechanics class but this video saved me
@thevelar7139
@thevelar7139 Год назад
No way no way no way , can i cry just bcuz i understand it ,daamnnn you did exellent explanation man ❤❤❤❤❤❤❤
@grindstm
@grindstm Год назад
This is the tensor visualization I have been waiting for. Thanks!
@NoNTr1v1aL
@NoNTr1v1aL Год назад
Absolutely amazing video!
@MysteriousSlip
@MysteriousSlip Год назад
Ooh man, exciting to find such a good video, but also scary to realize it is 8 months old already without part 2. 😭
@udiprod
@udiprod Год назад
Thanks! Part 2 should be ready in a few weeks.
@idrissmo418
@idrissmo418 Год назад
finally, a better explanation than "tensors are a generalisation of scalars and vectors" nice
@EMLtheViewer
@EMLtheViewer Год назад
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!
@safaahamdan5668
@safaahamdan5668 7 месяцев назад
This video is most credible great fantastic representation of tensor ❤❤❤
@Ganerrr
@Ganerrr Год назад
i rlly like this style of video, keep it up!
@tfairfield42
@tfairfield42 Год назад
Can't wait for part 2!
@natan4238
@natan4238 5 месяцев назад
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
@us-Bahn
@us-Bahn 3 месяца назад
There’s room for much more graphic instruction in physics & math than what is conventionally used.
@BernardoMartins_
@BernardoMartins_ 6 месяцев назад
Beautiful clarity. Masterpiece.
@danielobambelo1411
@danielobambelo1411 Год назад
Yes, finally new video, havent even seen it but i know that it will be great, also those who say first are stupid.
@bassamxp
@bassamxp Год назад
This is totally magnificent ... thank you. I'll make sure my students follow this video and the channel
@markhuebner7580
@markhuebner7580 9 месяцев назад
Very quick and very insightful thank you!
@joserodrigomorenolopez6651
@joserodrigomorenolopez6651 Год назад
Excelent video, makes visual everything that needs to be visualized. Congrats
@gorgolyt
@gorgolyt 10 месяцев назад
Great explanation, fantastic work.
@najahsaeed2006
@najahsaeed2006 11 месяцев назад
Thank you so much for the great effort in this video, all the best, and keep it up
@fbkintanar
@fbkintanar Год назад
Nice visualization, it makes the details a lot more memorable.
@jameyatesmauriat6116
@jameyatesmauriat6116 8 месяцев назад
When seeing videos like this makes me think why i do search for books that make me understand things better
@jimparsons6803
@jimparsons6803 3 месяца назад
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.
@silent88coder
@silent88coder Год назад
Dude, this is MAGNIFICENT! (Although I can't help admitting that choosing pink for arrows makes it look kinda... well, let's say Freud would have loved it!)
@tamalchakraborty791
@tamalchakraborty791 6 месяцев назад
I can't but subscribe to this channel. Beautiful
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