I think, that the covariant basis varies with the coordinate system, and the contra varies opposite to it. Geometrically, is the thing that's varying against the coordinate system just the length/magnitude of $e^i$ when $e_i$ is multiplied by scalar? I know the algebraically how the contravariant and covariant basis are related as inverses. Anyways, if for instance I decide to change just one component in the covariant basis by trippling it is there anything if I were looking at it geoetrically that would appear to vary opposite to the transformation?
2026-03-26 04:30:39.1774499439
What's contravariant about contravariance
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