First-order tensors are vectors and so symmetry makes no sense in this case.
hello, I've got what is may be a silly question:
is a tensor of order one symmetric and skew-symmetric at the same time by strict application of the defintion of symmetry and skew-symmetry?
My question is: by the same strict logical interpretation of the definition, should we conclude that they are skew-symmetric too?
Skew-symmetric tensors are discussed on pg 91 but I can't get access to ths at the moment. In any event, B&G say that by logical interpretation they can conclude that degree 0 or 1 tensors must be symmetric. The same (vacuously true) argument implies that they must also be skew-symmetric.