I came across this question which asked us to come up with the "second order antisymmetric tensor associated with a vector" which was given in the problem. The components of the vector were coordinate dependent and the problem was to be solved in Cartesian coordinates. What I can't understand (and I can't find it anywhere) is what is meant by a tensor associated with a vector? What does the word associated imply here? Any help is appreciated. Thanks.
2026-02-23 05:57:34.1771826254
Associated Tensors.
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I found something that might be useful:
http://www.owlnet.rice.edu/~ceng501/Chap2.pdf
Look at "The vector of an antisymmetric tensor".
It appears to be a way to take the fact that in three dimensions an anti-symmetric tensor can be related to a vector. \begin{equation}\Omega_{ij} = \epsilon_{ijk} \omega_k\end{equation}