Introduction to Tensors

My tensor series is finally here! In this video, I introduce the concept of tensors. I begin by talking about scalars, then vectors, then rank-2 tensors (whose explanation takes up the bulk of the video since these are probably the most difficult to understand out of the three).

I then move on to define tensors (without specifying their transformation properties), after which I conclude the video with a short discussion on rank-3 tensors, which may be represented by 3-D matrices/arrays.

Questions/requests? Let me know in the comments!

Pre-requisites: You basically need to know what vectors, scalars, and matrices are. Nothing much more to it. A 1st-year Physics + Linear Algebra course should be enough.

Special thanks to my Patrons for supporting me at the $5 level or higher:
- Jose Lockhart
- Yuan Gao
- James Mark Wilson
- Marcin Maciejewski
- Sabre
- Jacob Soares
- Yenyo Pal
- Lisa Bouchard
- Bernardo Marques

#Tensors #TensorMath #TensorIntro

[FacultyofKhan]

If you all liked this video, then make sure to check out the remainder of my playlist on Tensors, because there's more where that came from!

[KeyMan]

I have a bachelor's degree in Physics but we didn't talk about Tensors much. This was an excellent introduction!

[CazoDK]

This is the best video about tensors on youtube. The only video that covers the actual definition of a tensor: a tensor in _m_-dimensional space at rank _n_ is a mathematical object with components _m^n_., which obeys some rules. Thank you.

[skudzer]

I have no idea what's going on, I just found this video in my recommended section, but I love the black background with the colored writing; it's very pleasing to the eyes.

[Abhisruta]

Your digitised handwriting is beautiful...this may be a Handwriting Tensor Analysis

[maurocruz]

You just broke me free from YEARS and years of misconceptions about what a tensor and its rank really are . Thank you.

[rahuldas]

Shit this 4 year old content is much better than all the videos I watched on Tensors till now ❤️😍

[eyeballs]

You just explained what my teacher failed to explain in 3 90 min lectures in 11 minuites. Thank you so much! :)

[KevinKuo]

It's a good day when Khan releases a video

[ahmedamr]

Finally! A clear and intuitive explanation of tensors. Great job man!

[MeepMu]

Thank you! You seem to be the only person on the internet who explains what a tensor is from the ground up, and actually gives a concrete example that can be followed and understood by someone who is new to the concept.

[JulieanGalak]

Perfect timing! I just hit the point in my self-study of electrodynamics where I needed to understand tensors. Please release this series quickly! :)

[enricoiraldo]

incredibly useful. In my ignorance so far I always struggled to really find a connection between simple dimensions such as temperature and vectors, always considering them “different topics on the maths book”, but it is now clear how they are linked together

[isma]

This is the most geometrically comprehensive explanation about TENSOR that I have seen on Youtube or books. Finally I realized why the vector's components on same direction can't be added. Thanks

[YourCRTube]

5:25 is why this explanation is the best - it tell you how they are used in practice!

[evandrogaio]

Amazing. An easy way to explain this amazing definition. Almost all students leave college without a good understand of this

[AniketSharmacodes]

I had two questions about tensors after a lecture at my class today,
1. Why are there 9 components and not just add resultant force to 3 component?
2. How is Tensor different from a Matrix?

This video answered both of these questions in a very clear and oriented manner. Thanks for understanding what students can be confused about and addressing it right in the first place.

[trixonx]

With this explanation even a chimpanzee can understand the concept. Very effective. One of the Best 11 mins of my life spent on YouTube!

[andcool]

Probably the best tensor video I 've come across to date. Very elegant and crystal clear explanation of the idea of tensor, especially by bringing up real-life examples of breaking down a rectangular steel beam.

[joluju]

Been wondering what it was for tens of years. At last, an explanation with no bs. Thank you so much.