Source: cirosantilli/a-linear-map-is-a-1-1-tensor
= A linear map is a (1,1) tensor
A linear map $A$ can be seen as a (1,1) <tensor> because:
$$
T(w, v*) = v* A w
$$
is a number, $v*$. is a <dual vector>, and <W> is a <vector>. Furthermoe, $T$ is linear in both $v*$ and $w$. All of this makes $T$ fullfill the definition of a (1,1) tensor.