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| | Invariance, Contravariance, Covariance |
 | | This discussion has focused on scalars and vectors, but the same ideas apply to tensors of any order. |
| | Of course, in the case of orthogonal cartesian coordinates the axes are, by definition, normal to constant coordinate surfaces, so the distinction between contravariant and covariant components vanishes. |
| | At this point people often wonder how we can talk about a vector being contravariant or covariant when the direction and magnitude of a vector (which are its defining properties) are actually invariant with respect to coordinate changes. |
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