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A comment on Why tensors? A beginner's perspective. Parent comment

Re:Why tensors? A beginner's perspective by cygx on Thursday March 10, 2022 @04:18PM (#30632588)
I'm aware. Though if we want to be more precise, that's about tensor fields, where the basis transformations of the underlying vector bundles (the tangent and cotangent bundle) are in turn induced by coordinate transformations of the base manifold.

However, physicists get introduced to tensors far earlier than any excursions into differential geometry when discussing rigid bodies.

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Re:Why tensors? A beginner's perspective by contravariant on Thursday March 10, 2022 @04:29PM (#30632738)
Yes I'd also call those tensor fields. The main point I'm trying to make is that the tensor transformation law only makes sense for such fields.
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Re:Why tensors? A beginner's perspective by cygx on Thursday March 10, 2022 @04:39PM (#30632840)
The terms co- and contravariant make sense on a purely algebraic basis, with components of tensors transforming 'the same as' or 'opposite to' the basis vectors. That the basis transformation is induced by transformations of some base manifold is incidental.
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Re:Why tensors? A beginner's perspective by ummonk on Thursday March 10, 2022 @05:00PM (#30633048)
Exactly. The fact that the bases are related to coordinates on the manifold is a property of differential geometry but the laws for transformation between bases are more general.
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