information:extraction
Superscripts and subscripts versus only subscripts

In terms of covariance and contravariance of vectors,

They transform contravariantly or covariantly, respectively, with respect to change of basis.

In recognition of this fact, the following notation uses the same symbol both for a vector or covector and its components, as in:

where v is the vector and v are its components (not the i th covector v), w is the covector and w are its components. The basis vector elements e i {\displaystyle e_{i}} are each column vectors, and the covector basis elements e i {\displaystyle e^{i}} are each row covectors. (See also § Abstract description; duality, below and the examples)

In the presence of a non-degenerate form (an isomorphism V → V, for instance a Riemannian metric or Minkowski metric), one can raise and lower indices.

A basis gives such a form (via the dual basis), hence when working on R with a Euclidean metric and a fixed orthonormal basis, one has the option to work with only subscripts.

However, if one changes coordinates, the way that coefficients change depends on the variance of the object, and one cannot ignore the distinction; see Covariance and contravariance of vectors.