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).roberto85 said:Homework Statement
Explain how it is possible to perform a contraction of the tensor
$[T^{βγ}_{δǫ}]$ in order to produce a scalar T
Homework Equations
The Attempt at a Solution
$[T^{βγ}_{δǫ}] [T_{βγ}^{δǫ}] = T$
Not sure if that is correct? Also not used the forums in a while so not sure I am using the LaTex correctly here.[/B]
Thanks Ray, i just edited the equation but can't 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?Ray Vickson said: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.
A tensor is a mathematical object that represents linear relationships between vectors, scalars, and other tensors. It is a generalization of a vector and can have multiple components in different directions.
Contracting a tensor involves multiplying its components in a specific way to produce a scalar value. This is done by summing over repeated indices in the tensor.
Contraction allows us to reduce the dimensionality of a tensor while still preserving important information. It is used in many areas of physics and engineering, such as in the study of stress and strain in materials.
Yes, a tensor can be contracted multiple times to produce a scalar value. Each contraction involves summing over repeated indices, so the number of contractions will depend on the number of repeated indices in the tensor.
Contraction of a tensor can be seen as a generalization of matrix multiplication. In fact, a tensor of rank 2 can be represented as a matrix, and its contraction can be calculated using the same rules as matrix multiplication.