Tensor
ฝัง
- เผยแพร่เมื่อ 2 ก.ค. 2022
- [ Clarification ]
Tensors could be written as "scalar" "vector" "matrix" etc.. but "scalar" "vector" "matrix" aren't always tensors.
This is because scalar vector matrix are more of mathematical definitions whereas tensor describes a physical quantity. "Tensor" relates to the word "tension".
I explained about the tensor for Physics and Engineering students.
I mainly tried to relate with General relativity course.
Stress tensor, energy-stress tensor and momentum-stress tensor are also explained.
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[ Clarification 1]
Tensors could be written as "scalar" "vector" "matrix" etc.. but "scalar" "vector" "matrix" aren't always tensors.
This is because scalar vector matrix are more of mathematical definitions whereas tensor describes a physical quantity. "Tensor" relates to the word "tension".
[ Clarification 2]
At 6:20, I used "sigma yz". Some textbook might show you as "sigma zy" . Those are just conventional. It doesn't matter much in which way you want to write. But I prefer my convention "sigma yz" because it works well as a transformation as shown near end of this video :)
I've put quite an effort into making this video, but I'm not getting that many subscribers 😢
If this video helped you, pleaseeeee subscribe to my channel. It really motivates me ! :)
I see you here already connecting the “tensile-strength” I mentioned with the concept. More power to you man!
I'm confused by your first clarification. A tensor does not always describe a physical quantity, because (mathematically) it is just something that lives in a tensor product of vector spaces or vector bundles. For example, a connection 1-form or gauge field is a rank 1 tensor, but it certainly isn't physical.
I think a good point to also remember is that an indexed object like T_{...}^{...} which we often call a tensor in physics is not actually a tensor, but the components of a tensor with respect to a choice of basis. This is useful when one thinks of things in terms of differential geometry, where we work on a local coordinate patch which then gives us a basis (of the partial derivatives w.r.t. these coordinates) in the tangent spaces on that patch. In this sense, when a coordinate change is made on the patch, the tensor T is invariant and only the components T_{...}^{...} change because the change of coordinates changes the basis vectors.
Another thing that is maybe less useful in physics, but interesting mathematically is the universal property definition of the tensor product (doing things with tensors without referring to a basis can be quite instructive and useful mathematically, it shows what things are 'natural'). Maybe someone here finds this interesting
It sounds like you understand tensors well! I did clarify through the comment that it is one way, but not the other way. This video is for the beginners who have no ideas about tensors. Sometimes we need more friendly and easy explanation, then go deeper after. Thats my way of teaching :)
Broh..........❤❤
My brain is flying now....
Thanks for the wonderful video
I subscribed your channel
Do more videos like this ❤❤
It's a good start. Since (some) tensors are directly rooted in geometry@@ReumiChannel While (m,n) tensors are products from vectors that are transformed covariantly and contravariantly. So the exponentiation of indices is done to indicate that something transforms contravariantly, while the lowering of indices is done to indicate that something transforms covariantly.
So a vector of a ordinary vector space would have its components transform contravariantly, and therefore have its index exponentiated while a covector of a dual vector space would have its components index being lowered. This convention is very powerful when combined with Einstein's notation, because it enables us to take some shortcuts in math.
Also i'm not sure, about this but should the z-z component of the 3D stress tensor not be negative according to the orientation of the z-axis since it would point downwards compared to the z-axis that points upwards.
Anyways. Good video. And it is a neat idea to start somewhere where most of us can understand the topic clearly, and also use it for simple practical purposes. Since not every person who has to learn to use tensors needs to learn about tensor spaces.
Sir, you have no idea how much this has helped me reinforced my understanding of Tensor...thank you! Sending God's Blessings Always🙏🏽
Wow. Thank you so much for such a great compliment
Mad lad, this is so well produced and somehow embedded some kind of humor in it. Very educational and it’s fun to watch idk why! This is some explaining skill my school professor should have at least half of it.
Wow thank you so much for such a great compliment ! :)
I love your teaching style. Thank you for making these videos!
I have seen a LOT of tensor videos on TH-cam, but this explains it best.
Thanks a lot !
Sir please continue the series!! It's really helpful for my graduate course understanding!🙏🏻🙏🏻❤❤❤
Thanks! It motivates me a lot :)
Let me know if any topics
Nice job. I love that you give lots of examples. A lot of authors stay abstract and that is not a good teaching methodology. Thank you.
I feel you. I always had the same struggle when i was a student. We need many examples!
I am glad you explained the stress tensor properly. Usually people just dump the stress tensor example , as if it should be obvious since birth. Not everybody is smart enough to follow. Explaining step by step like this is very helpful. Thank you.
Please continue to make more videos on Tensors. There is a serous lack of INTUITIVE (very important word) explanations on Tensors.
Thank you for the compliment ! Yes, i will :) indeed 'intuitive' explanation is important
Pedagogical genius!!
My presentation skills are not good your slides and way of presenting the stuff is really inspiring.
My QM 2 Prof literally taught us the quantization of electromagnetic field without even teaching field tensors. these lectures are amazing..
Thank you so much sir!! 🤩
Holy wow. I thank you for such a great compliment. Let me know if you have some ideas of what i should explain next. I consider peoples suggestions.
This is awesome! Very well explained. Thanks
Wonderful video. Thanks for making it!
Brilliant, full of humour, educational, a gem!
this is the best explanation of tensors i've seen and i've been looking for a long while! Thanks!
Great explanation!
Best explanation man !!
Nice 👍
Very Nice!!!
Ty! Great video! It will help me with electromagnetic field tensor.
I have started my machine learning and this is one of the outstanding videos on tensor introduction. Thank you sir😃
I'm glad it helped !
Great videos! Please keep making more, they are very very informative and absolutely awesome for learning physics and mathematics! Thank you so much!
Yes, for sure. Thank you :)
Love your explanation
Thank you
Beautiful clarity. Thank you.
I thank you ^^
This is the second video from Reumi that i've watched of recent. Absolutely excellent tuition accompanied by superb and concise "blackboard descriptions" with good examples. Thank you so much. (From South Africa.)
Haha. The videos made in this small village in Canada reached South Africa ! Yay scientists !
Very good, thanks a lot
So finally I understand the tensor , keep doing good work and make series on all concepts about tensors
Thanks ! a subscription would help :D
Amazing video thank you so much
Thanks for the compliment !
excellent sir! one of the best videos on the net. You have a knack to explain difficult concepts in a great way! Thank you
I thank you for such a great compliment. You motivated me a lot :) let me know if you want me to cover on something
@@ReumiChannel Dear Sir, I am old retired engineer. When I was young, I always wanted to know the history or background on how the Laplace Transform came into existence. Our professor use to say just use the method. It works. I don't know if this topic would be popular. If you think it is and have knowledge to explain how the Laplace Transform is derived or came about it would be interesting. Thank you gain.
@@sollyismail1909 Oh you are our academic senior! I salute you, and thank you for having developed this world for us. Before I explain about Laplacian, I have to explain Fourier. But I was planning to make one about Fourier in the next year. So plz stay tuned until then, if it's not urgent :)
very good
12:23 Connection bridge, eigen value, transformation matrix, convolution these are all from the same village
Mega dank Vid. mate!!! Wonderful job explaining, helped a lot.
Thanks a lot for the comment, mate !
this is awesome
Sir actually you made my life, you cleared all my basic doubts thank you sir. I want you to post still videos on tensors like from 'GR' and still more on tensors. Thank you sir
Haha. Thanks. I will for sure. Im just on a break atm
This was extremely helpful!! Thank you!
I thank you for your great comment !
Thank you.
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감사합니다
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7:20 Just so you know, not only you gave an intuitive analogy, you actually explained the whole deal behind coming up with such an object, where the very exact analogy is the reason with only the specific attributes stripped down to something general, which seems to also be universal too. As far as the set of all possible motions that any physical objects `could` have, is a conceivable thing to consider, a Turing machine is universal but does not represent the whole of computational universality. There exists another set which refers to the set of all the possible motions that `could be caused` to have in any of the attributes of the substrates that we deal with, and then a Turing machine even could be programmed to simulate that although with probably a runtime length of trillion years. However the principle would still be something like you just used to explain, and we don't necessarily have to go any lower than `something like` with objects like these.
Consider the word `tensile strength` and you should get the reference connection. Although I don't see anything doing that, but this essentially tells us already that computation is physical, so look into that.
Good work!
Thanks for the deep comment and your advise. It is true that i sometimes say things that might not exactly be true, but sometimes its more important to make people roughly understand first, before bringing the exact descriptions, haha :)
@@ReumiChannel When is anything exactly true other than the ones we know to be true? Wait do we know those things that are true to be exactly true? I am being silly here intentionally because we don’t know anything to be true neither exactly nor approximately as of today at last. But it’s fine, because the goal is not to aim for the truth if that thing (truth) is something even real, instead what we want is error correction and conjectures, not even tests. Then all that could to really aimed for is some way of knowing that our conjectures did something to the real objects, so we creatively conjecture another thing that would let us know and here we are going to get twice the information than simple testable predictions, because (a) we learn whether anything refutes our theories, (b) of illegal then we also know what kinds of things went wrong. Unless the laws of physics really prohibits something, we could do just do it (or have it done), given the knowledge through explanations of the kinds I mentioned. And that is probably close to something that could closely reach that “exact” truth that you mentioned, but I don’t see any other possible way of satisfying that goal. Lol Or simply not set goals in the first place, at least not of the kind that requires us to be absolute rather than abstract.
Btw by abstract i meant a set of principles that allows us (personally) to make contact with reality and find the regularities that would allow us (collectively) create more and more knowledge.
Great explanation..
It is a great aid for my tomorrow's seminar❤
Thank you so much for the clarity of concept🎉
Your welcome!
What the EFE doesn't show is that the Einstein tensor G(mu)(nu) is really a combination of a rank 0 tensor (Ricci scalar) and a rank (0,2) tensor (Ricci tensor)
... which in turn is a combination of a set of rank (1,3) tensors (Riemann curvature tensor)
... which in turn is a combination of many rank (1,2) tensors (Christoffel symbols) and their partial derivatives
... which in turn is a combination of partial derivatives of a rank (0,2) tensor (metric tensor, g(mu)(nu) )
Now you know why GR is so challenging. Its not hard conceptually understanding of Einstein's theory of gravity (ie GR). It's just really tedious work computing the all the tensors, even with the nice helpful symmetries and identities to reduce their distinct number of independent components.
Great explanation.
But what is the meaning of the splitted rank like (1,2) ?
Thats a great question. There are tensors and dual tensors. I have a video about dual vectors. You could have a look. The splitting is related to that
You were magnificent Reumi ill never forget you as long as i live
haha. thank you so much. You won't forget, cuz I'm gonna someday become the best educator in the world !
Great video. Can you also explain vectors covectors pairs?
Thanks. Ive already covered Dual vector(covector). I recommend watching that
Hi, what is the meaning of the separation when writing the rank of the tensor like (1,2). I understand pretty much everything you said, but I can't seem to realize what the reason for the subscript versus the superscript is.
There are something called "Dual tensor" "Dual vector". Those are with the subscripts.
Watch these two videos?
th-cam.com/video/8ZmqL_nLvjM/w-d-xo.html&ab_channel=Reumi%27sworld
th-cam.com/video/OoT8kty3HPA/w-d-xo.html&ab_channel=Reumi%27sworld
13:43 this is the Hilbert field equation.
Hello, at 6:20 you denote the shear stress of the forces y-component acting on the face perpendicular to the z direction as sigma_yz, yet some text books and sources would seem to have this notation flipped (i.e. sigma_zy). For example at 4:25 of this video (th-cam.com/video/uaQeXi4E7gA/w-d-xo.html). I was wondering (if I am understanding this correctly) is this a notation-convention difference or am I misunderstanding something?
The other way is fine :). Its just conventional. But i think my way (sigma yz) is better than (sigma zy) because it works nicely as the transformation matrix (near the end of the video)
@@ReumiChannel Thank you so much for the clarification! Your videos have a wonderful help :)
Okay, but at 09:00 why is it Rank (0,2)? And not Rank (2,0) did I miss that part? What ist the difference between (0,2) and (2,0)?
yes you missed a part :)
me watching this instead of studying for my linear algebra and geometry exam:
Oh no. U should study! Watch this later
sorry but i didn't understood how you said the tensors are 2D and 5D in 2nd and 3rd example please explain it
Inside the brackets, there are variables. Its like f(x), f(x,y) and etc
ok thank you
@@ReumiChannel can you recommend a few book to understand the tensors properly because the del mu of four vectors giving rise to metric tensor and some times different dirac tensor is pretty hard for me to understand
@@amitsirsstudent7111 I'm sorry. I also learned it in a hard way. I cannot think of a good one to suggest. Maybe "Griffiths" ..? Perhaps these two videos that I made could help?
th-cam.com/video/OoT8kty3HPA/w-d-xo.html&ab_channel=Reumi%27sworld
th-cam.com/video/J7-vJrRxR40/w-d-xo.html&ab_channel=Reumi%27sworld
not understand pl. made it very simple
??