Undergrad Question regarding actual computation of tensor at point (Self Study)

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The discussion centers on the computation of tensor components and the importance of considering the manifold structure in these calculations. The poster seeks validation on their approach to determining nonzero components of a tensor and the correctness of their overall computation process. Feedback received confirms that the inquiries are appropriate for the forum. The conversation emphasizes the relevance of understanding manifold structures in tensor analysis. Overall, the poster is encouraged by the positive response to their questions.
Amateur659
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Hello all,

I am hoping to get some feedback on the manner in which I performed computations towards solving the following problem.

question.PNG


There are a couple specific points which I am not confident of:
1. Did I properly account for the manifold structure in my computation of the nonzero components?
2. Is the general process by which I compute each tensor component correct?
IMG_20220213_010056272.jpg


Finally, please let me know if I am making a mistake posting such questions here.

Thank you for your time and feedback!
 

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It looks fine.
 
Awesome, thanks for the feedback.
 

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