Results 1 to 6 of 6

Math Help - Order one tensor

  1. #1
    Junior Member
    Joined
    Feb 2010
    Posts
    37

    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?
    Last edited by facenian; June 29th 2011 at 02:53 AM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member
    Joined
    May 2010
    From
    Los Angeles, California
    Posts
    274
    Thanks
    1

    Re: Order one tensor

    First-order tensors are vectors and so symmetry makes no sense in this case.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Feb 2010
    Posts
    37

    Re: Order one tensor

    Quote Originally Posted by ojones View Post
    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?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Senior Member
    Joined
    May 2010
    From
    Los Angeles, California
    Posts
    274
    Thanks
    1

    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?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Junior Member
    Joined
    Feb 2010
    Posts
    37

    Re: Order one tensor

    the book is "Tensor Analysis on Manifolds" Chapter II, page 88 (1980 edition)
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Senior Member
    Joined
    May 2010
    From
    Los Angeles, California
    Posts
    274
    Thanks
    1

    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.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Tensor
    Posted in the Advanced Algebra Forum
    Replies: 4
    Last Post: December 15th 2009, 10:24 AM
  2. Tensor
    Posted in the Calculus Forum
    Replies: 0
    Last Post: October 1st 2009, 09:57 AM
  3. Zm tensor Zn
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: March 24th 2009, 11:47 AM
  4. Tensor Divergence
    Posted in the Calculus Forum
    Replies: 0
    Last Post: January 11th 2009, 07:10 PM
  5. Tensor
    Posted in the Advanced Applied Math Forum
    Replies: 1
    Last Post: February 27th 2008, 06:47 PM

Search Tags


/mathhelpforum @mathhelpforum