Understand Tensors: Difference from Matrices

[Silviu]

Hello! I am not really sure I understand the idea of tensors and the difference between them and normal matrices, for example (for rank 2 tensors). Can someone explain this to me, or give me a good resource for this? I don't want a complete introduction to GR math, I just want to understand the idea of tensors for now. Thank you!

 

[fresh_42]

https://www.physicsforums.com/threads/a-question-about-tensors.889777/#post-5597259

What is additionally important especially in physics, is the fact that the vector spaces involved can also be dual vector spaces, i.e. vector spaces of linear mappings to the field: https://en.wikipedia.org/wiki/Covariance_and_contravariance_of_vectors.

 

[PeterDonis]

Explaining tensors in general is too much for a PF thread. You might try Sean Carroll's online lecture notes on GR:

https://arxiv.org/abs/gr-qc/9712019

Chapter 1 discusses tensors.

 

[Nugatory]

There's also the web version of Carroll's material, starting here: https://www.preposterousuniverse.com/grnotes/
OP may find that the "no-nonsense introduction" better meets their needs, but should be warned that some corners are being cut there.