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Seeking a logarithmic operator for a 4th order tensor
I don't know whether this question has an answer, but I'd like to see what you all think:
Does anyone know whether or not the following operation is meaningful, whether it is described and defined algorithmically somewhere, and / or how to do it?
ln(Aij) = Bkm ln(Cijkm)
A and B are second order tensors
C is a 4th order tensor
The left hand side involves the natural logarithm of the 2nd order tensor A, which is no problem.
The right hand side involves the natural log of the 4th order tensor C, which I have never encountered before.
I greatly appreciate any leads you can provide.