Find the effect of a rotation by about the -axis on the tensor
Hence show that the most general isotropic tensor of rank 2 is , where is an arbitrary scalar.
Prove that there is no non-zero isotropic vector, and write down without proof the most general isotropic tensor of rank 3 .
Deduce that if is an isotropic tensor then the following results hold, for some scalars and : (i) ; (ii) ; (iii) .
Verify these three results in the case , expressing and in terms of and .