Re: Order of indices in tensors...

From: Rene Meyer (meyr2_at_web.de)
Date: 08/25/04 

Date: 25 Aug 2004 09:40:04 -0400

"Flip Tomato" <flipt@stanford.edu> wrote in message news:<cgbmkh$2rv$1@news.Stanford.EDU>...
> What is the significance of the order of indices in a tensor? I understand
> that the convention is for upper indices to sum with lower indices and vice
> versa when the tensor acts on the appropriate object, however, what is the
> significance of having the upper index listed first or the lower index
> listed first (horizontally)?

Hi Flip,

you should distinguish between two aspects:

1) Tensors can be symmetric, antisymmetric or without any symmetry
within their indices. For example, the metric tensor is symmetric, the
Levi-Civita tensor antisymmetric in all indices. Can you write a
tensor without special symmetry? [1]

2) If you are dealing with tensors of order 2, i.e. with two indices,
you can write them down as a matrix, i.e. the metric tensor. Then, the
order of writing of the indices also becomes important when you are
contracting tensors by doing matrix multiplication.

Rene.

[1] T^abc_def = delta^a_d delta^b_e delta^c_f
                - delta^a_e delta^b_d delta^c_f
                - delta^a_f delta^b_d delta^c_e

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