  Classical tensors, the familiar mathematical objects denoted by symbols such
as $t_{i}$, $t^{ij}$ and $t_{k}^{ij}$, are usually interpreted either as
'coordinatizable objects' with coordinates changing in a specific way under a
change of coordinate system or as elements of tensor spaces of the form
$V^{\otimes n}\otimes\left(V^{*}\right)^{\otimes m}$. An alternative
interpretation of classical tensors as linear tensor maps of the form
$V^{\otimes m}\rightarrow V^{\otimes n}$ is presented here. In this
interpretation, tensor multiplication is seen as generalized function
composition. Representations of classical tensors by means of arrays are also
considered.
