Tensor-vector identity 2
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Let be a vector field and let be a second-order tensor field. Let and be two arbitrary vectors. Show that
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Proof:
Using the identity
we have
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From the identity
,
we have
.
Since is constant, , and we have
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From the relation
we have
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Using the relation , we
get
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Therefore, the final form of the first term is
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For the second term, from the identity
we get,
.
Since is constant, , and we have
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From the definition
, we get
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Therefore, the final form of the second term is
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Adding the two terms, we get
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Therefore,
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