3 ms·
Since these are Euclidean spaces, the difference between contravariant and covariant indices is non-existent. So it doesn't matter whether the indices are upsta
by cabinpark 12y ago
Since these are Euclidean spaces, the difference between contravariant and covariant indices is non-existent. So it doesn't matter whether the indices are upstairs or downstairs.
- JadeNB 12y agoI would say not 'nonexistent', but rather 'avoidable'; or, even better, that there is an isomorphism in an appropriate sense. (Compare the situation for strings and lists of characters; the types are isomorphic, but I wouldn't say that the difference between them is non-existent!)
- cabinpark 12y agoTrue. I'm just a lazy relativist though ;)
- sdenton4 12y agoYeah, but I find that -- like dimensional analysis -- keeping careful track of what's upstairs and downstairs can help me keep a computation from going off the rails.