Results 1 to 2 of 2

Math Help - Trace of a Tensor

  1. #1
    Newbie
    Joined
    Nov 2012
    From
    Indiana
    Posts
    1

    Trace of a Tensor

    I am not sure which category this goes in but I thought this fit best.

    I have a tensor x tensor x (when x is a vector)

    What would be the trace of this tensor?

    So tr(x tensor x)

    I thought it would be x ∙ x.

    Thanks
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,707
    Thanks
    1470

    Re: Trace of a Tensor

    If, for example, x= ai+ bj+ ck, in some coordinate system then x tensor x is represented, in that same coordinate system by \begin{bmatrix}a^2 & ab & ac \\ ab & b^2 & bc \\ ac & bc & c^2\end{bmatrix}. Yes, the trace of that is x\cdot x= a^2+ b^2+ c^2.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. trace
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: December 1st 2010, 02:27 PM
  2. Trace of a tensor product
    Posted in the Advanced Algebra Forum
    Replies: 4
    Last Post: March 26th 2010, 03:15 AM
  3. Trace
    Posted in the Advanced Algebra Forum
    Replies: 0
    Last Post: December 14th 2009, 12:08 PM
  4. Proving adj(a^trace)=[adj(a)]^trace?
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: September 24th 2009, 10:55 PM
  5. Trace of A squared linear function of A tensor A???
    Posted in the Advanced Algebra Forum
    Replies: 6
    Last Post: August 4th 2007, 04:13 AM

Search Tags


/mathhelpforum @mathhelpforum