= Tensor
{wiki}
A <multilinear form> with a <domain (function)> that looks like:
$$
V^m \times {V*}^n \to \R
$$
where $V*$ is the <dual space>.
Because a tensor is a <multilinear form>, it can be fully specified by how it act on all combinations of basis sets, which can be done in terms of components. We refer to each component as:
$$
T_{i_1 \ldots i_m}^{j_1 \ldots j_n} = T(e_{i_1}, \ldots, e_{i_m}, e^{j_1}, \ldots, e^{j_m})
$$
where we remember that the raised indices refer <dual vector>.
Some examples:
* <levi-Civita symbol as a tensor>{child}
* <a linear map is a (1,1) tensor>