# Thread: Order one tensor

1. ## Order one tensor

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?

2. ## Re: Order one tensor

First-order tensors are vectors and so symmetry makes no sense in this case.

3. ## Re: Order one tensor

Originally Posted by ojones
First-order tensors are vectors and so symmetry makes no sense in this case.
Hello, thanks for your response but I think you have to reconsider your concept of symmetry. I qoute Bishop and Golberg saying "By convention(or strict logical interpretation of the definition) we agree that tensors of degree 0 or 1 are symmetric"
My question is: by the same strict logical interpretation of the definition, should we conclude that they are skew-symmetric too?

4. ## Re: Order one tensor

I don't need to reconsider the concept because we're talking about a convention. What's the book title and page number for B&G?

5. ## Re: Order one tensor

the book is "Tensor Analysis on Manifolds" Chapter II, page 88 (1980 edition)

6. ## Re: Order one tensor

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.