From what I understood, a vector can be either covariant or contravariant. Which one this is will depend on how the coordinates of this vector transform under a coordinate transformation. Let's take a look at the electric field then:(adsbygoogle = window.adsbygoogle || []).push({});

##\vec{E}=-\nabla{V}##, so here it looks as if the electric field is covariant.

However if we have a particle in space, it will accelerate due to this electric field and now the electric field can be expressed as :

##\vec{E}=c\vec{a}## where ##\vec{a}## is contravariant , and so here it looks like the electric field is contravariant.

So is my understanding about vectors being either covariant or contravariant incorrect?

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# Contra and covariance question

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