2
votes
0answers
65 views

Is there any distinction between these products: scalar, dot, inner? [migrated]

I hope you will forgive a math question that comes up in physics contexts where language is loose. There is a product which can be defined on a vector space that takes two vectors and returns a ...
9
votes
3answers
1k views

What does the dual of a tensor mean (e.g. dual stress tensor in relativistic ED)?

I know what the dual of a vector means (as a map to its field), and I am also aware of of the definition a dual of a tensor as, $$F^{*ij} = \frac{1}{2} \epsilon^{ijkl} F_{kl}\tag{1}$$ I just don't ...
17
votes
4answers
4k views

Are matrices and second rank tensors the same thing?

Tensors are mathematical objects that are needed in physics to define certain quantities. I have a couple of questions regarding them that need to be clarified: 1-Are matrices and second rank tensors ...