Timeline for Why is this step in proving that a partial derivative of a vector is not a tensor illegal?
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| Nov 17, 2022 at 4:26 | comment | added | J Peterson | @NX37B. Technically any linear combination of the basis vectors, or tensor products of the basis vectors, is a tensor. However the differential of a vector field is not a “good” tensor in that $\partial_j v^i \pmb{e}_i \otimes \pmb{e}^j \neq \partial’_j v’^i \pmb{e}’_i \otimes \pmb{e}’^j$. | |
| Nov 8, 2022 at 18:12 | comment | added | Ghoster | @NX37B The cross in a circle is a tensor product. | |
| Nov 8, 2022 at 15:02 | comment | added | NX37B | I am sorry I do not understand. My course notes and everywhere else I looked at say that the partial derivative of a vector is not a tensor. I am only familiar with the component representation of tensors, and I've never seen the 'cross in a circle' operation that you used here, what is it? | |
| Nov 8, 2022 at 14:52 | history | answered | basics | CC BY-SA 4.0 |