Are Order 1 Alternating Tensors Different from Normal Tensors?

[yifli]

I don't understand how order 1 alternating tensors fit the definition of alternating tensors. I think the order has to be at least 2 for the definition to make sense because only then can we talk about permutation.

So I think there's no difference between order 1 alternating tensors and normal order 1 tensors, correct?

 

[WannabeNewton]

When you say alternating do you mean anti - symmetric? Anyways, yes you are correct in saying that a 1 - tensor is not anti - symmetric because for a tensor to be anti - symmetric there needs to be at least one pair of indeces such that the tensor changes sign when the indeces in the pair are swapped in which case it is anti - symmetric in those two indeces.

 

[mathwonk]

remember truth by empty hypothesis?