Welcome to our community

Be a part of something great, join today!

Tensors and Indices

ALIENSUN

New member
Jul 27, 2018
1
Can anyone explain exactly what the position of indices in a tensor represent? What difference does it make between having two superscript indices, two subscript ones and one of each?
 

GJA

Well-known member
MHB Math Scholar
Jan 16, 2013
256
Hi Aliensun,

Not sure if you're still interested in this post, so I will keep my answer brief for now. In short, the location of the indices indicate how the components of the given tensor transform under a change of basis in the underlying vector space. Lower indices indicate a covariant transformation; i.e., a change in the tensor's components that behaves in the same manner as the change of basis itself. Upper indices indicate a contravariant transformation; i.e., a change in the tensor's components that behaves according to the inverse of the change of basis itself.

This is likely to be a bit vague. I am happy to discuss the topic further if you're still interested.