Tensors as a Sum of Symmetric and Antisymmetric Tensors

In the last tensor video, I mentioned second rank tensors can be expressed as a sum of a symmetric tensor and an antisymmetric tensor. Today we prove that.

[RafaellxDZ]

2:31
My cat does the same thing when he's asking for food

[paoloazzini]

1:52 yeah i'm really into hentai-symmetric tensors

[billfeatherstone]

Thanks Andrew .. I have been studying tensors in books for ten years and its really becoming clearer as I enjoy your presentations

[andrewpriest]

"The way you can tell, is because of the way that it is"
lol

[subscribetopewdiepie]

9:49 Hold on a sec am I considered to be a tensor boi from now on
Damn can’t wait to flux on my virgin friends

[loganjames]

Anyone else in high school and have no idea what's going on or why they're watching this video?

[Ksdpm]

Absolute quality
keep up the good work man
Btw any chance to do group theory and Lie group in the future?

[lukesaunders]

I find putting round and square brackets round the symmetric and anti-symmetric indices very useful, good for when a subset of the indices has that property etc. I lose track otherwise when we start using 3 or more indices!

[XEwgf]

"What's going on smart people?"

ok looks like you don't need me here

[Tom-vuwr]

4:40 what the textbook I was learning tensors from said

[nanocount]

4:07 Aren't the indices of the last term supposed to be swapped?

[pugazharasuad]

1.) Set 0.25x speed,
2.) Head to 0:03
3.) Watch

[danieljensen]

Thanks for doing this homework problem for me.

[lambdamax]

Do muscles get tense when performing tensor analysis calculations?

[oni]

I may come off as pedantic but shouldn't the inertia tensor at 1:46 have upper indices because it is defined to transform contravariantly?

[Amit-gi]

Coordinates generalized to vectors, vectors generalized to matrices, matrices generalized to ranked tensors, ranked tensors generalized to tensors. Mathematics is the whole business of generalisation

[KyleDB]

I guess this extends to higher rank tensors, so they are always sums of tensors which are symmetric and antisymmetric to any pair of indices?

It also looks like this does depend on whether the object actually transforms like a tensor, i.e. you could say the same thing about any N-dimensional matrix right?

[AngelMartinez-vgnz]

All you need Andrew is lecture notes in your hand to be a professor.

[hairythetablefry]

Can you do a video on kinematics please or is that too advanced for you

[RockieAtlas]

I'm going to remember how to do it and show people so they can be mesmerized and when I could of gained complex knowledge in something outside my major 😂