If we assume a Cartesian basis, we can write the given relation in index
notation as
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where is the Levi-Civita (permutation) symbol.
Since is does not depend upon the position we can write
-
Define
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Then,
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Expanding, we get
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Expanding further, we get three equations
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or,
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or,
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Therefore,
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Also, by symmetry,
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Therefore we may write,
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Reverting back to direct tensor notation, we get
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