# Contraction of a tensor to produce scalar

1. Dec 1, 2017

### roberto85

1. The problem statement, all variables and given/known data
Explain how it is possible to perform a contraction of the tensor
$T^{\beta \gamma}_{\delta \epsilon}$ in order to produce a scalar T

2. Relevant equations

3. The attempt at a solution
$$T^{\beta \gamma}_{\delta \epsilon}T_{\beta \gamma}^{\delta \epsilon}=T$$

Not sure if that is correct? Also not used the forums in a while so not sure im using the LaTex correctly here.

Last edited: Dec 1, 2017
2. Dec 1, 2017

### Ray Vickson

You can tell you are not using LaTeX properly, just by reading your own message. For in-line formulas and equations, use "# #" (with no space between the two #s) instead of "$" at the start and end of you object. Also: spell out the actual names of the Greek symbols, so that β is "\beta" (backslash + 'beta'), etc. For your first formula this gives $T^{\beta \gamma}_{\delta \omicron}$ (if the object "ǫ" is an $\omicron$---I could not figure it out). For a displayed formula or equation, just use two$ signs (with no space between them) at the start and the end. That gives
$$T^{\beta \gamma}_{\delta \omicron}T_{\beta \gamma}^{\delta \omicron} = T$$
You can right-click on a formula or equation and ask for display as TeX, to see the commands used in the above two examples.

3. Dec 1, 2017

### roberto85

Thanks Ray, i just edited the equation but cant see why its not displaying correctly? edit: i see now, sorry. Is that correct to say then that the covariant multiplied by the contravariant will reduce it to a scalar?