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Homework Statement
if BijkAjk is a vector for all symmetric tensors Ajk, (but Bijk is not necessarily a tensor),
what are the properties of Bijk under rotations of the basis/coordinate axes?
Homework Equations
The Attempt at a Solution
I am not sure what the question is looking for... though I can say that
BijkAjk=BijkAkj(by symmetry of Ajk)=BikjAjk(by relabeling dummy suffices)
Since Ajk is an arbitrary symmetric matrix, they cancel, giving Bijk=Bikj
So Bijk is symmetric wrt the last 2 suffices...
Thanks in advance!
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