Solving Tensor Problem: Need Help Now!

[samson07]

Spent several hours in the library on this and i have no idea how to do...

please help I'm going to burst out with tears soon...

 

[Fredrik]

I can't make sense of any of that. Does A_ijkl=F_ijkl(a_m) mean that A_ijkl is the result of letting F_ijkl act on a_m? Then why doesn't A have five indices instead of four? Is a_m a vector or a component of a vector? Why doesn't m appear anywhere on the right? What are the definitions of A·B and A^-1? (I haven't seen either defined for tensors with 4 indices). Does A denote the tensor and A_ijkl its components in a coordinate system? Then what does A (no indices, not bold) denote?

 

[Tinyboss]

Looks to me like F just takes a six-tuple of coefficients (what kind, who knows?) and spits out a rank-4 tensor. In other words, F is some six-parameter family of tensors. I suppose the answers will be in terms of the a_i's and b_i's (i=1,...,6).