Tensor Conventions for Contravariant and Covariant Notation

[quasar987]

If a tensor acts on V x V* x V, do we say that it is

i. 1 time contravariant, 1 time covariant, then 1 time contravariant

ii. 2 times contravariant, 1 time covariant

iii. 1 time covariantt, 2 times contravariant

vi. there is no convention

 

[dextercioby]

The tensor is neithzer covariant nor contravariant, it's an invariant geometrical object. However, in the canonical basis of the tensor product of spaces under discussion its components are

T=T^{i}{}_{j}{}^{k} e_{i}\otimes e^{j}\otimes e_{k}

So which one is it ?i, ii, iii or iv ?