Are Order 1 Alternating Tensors Different from Normal Tensors?

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Order 1 alternating tensors do not differ from normal order 1 tensors, as they lack the necessary structure for anti-symmetry. The definition of alternating tensors requires at least order 2, where permutation of indices can occur. In the case of order 1 tensors, there are no pairs of indices to swap, thus they cannot exhibit anti-symmetry. The discussion clarifies that the term "alternating" in this context does not apply to order 1 tensors.

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yifli
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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?
 
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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.
 
remember truth by empty hypothesis?
 

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