The change from covariant to contravariant or vice-versa is defined as $$v_{i}=g_{ij}v^j$$ The component of a dyad, gij in general is given by $${g}_{ij} = \vec{e}^i . \vec{e}^j$$ here $$e⃗^ i\,\text{ and }\, e⃗^ j $$ Contravariant basis vectors a similar statement can be defined for a covariant basis vector
Why has the superscript of the contravariant basis replaced by the subscript for the dyad component, gij.Is it just a notation..as $$\vec{e}^i . \vec{e}^j$$ is just scalar product of two vectors which is just a scalar, hence its neither contravariant or covariant...or am I missing something
This is a repost of a part of another post...I have the same question so I am asking again.