1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Demonstrate the matrix represents a 2nd order tensor

Tags:
  1. Oct 18, 2015 #1
    1. The problem statement, all variables and given/known data
    Demonstrate that matrix ##T## represents a 2nd order tensor

    ##T = \pmatrix{ x_2^2 && -x_1x_2 \\ -x_1x_2 && x_1^2}##
    2. Relevant equations

    To show that something is a tensor, it must transform by ##T_{ij}' = L_{il}L_{jm}T_{lm}##. I cannot find a neat general form for ##T_{ij}##
    3. The attempt at a solution

    This has been difficult to do, so I'm running of options. A hint may be helpful.
     
  2. jcsd
  3. Oct 18, 2015 #2

    fzero

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Try ##T_{ij} = - x_i x_j + \delta_{ij} A##. Compute ##A## by comparing the trace of this expression with the trace of that matrix.
     
  4. Oct 19, 2015 #3
    Thanks. The A is going to be ##x_kx_k##. This is a scalar, so the transformation looks correct.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Demonstrate the matrix represents a 2nd order tensor
  1. Tensor for a matrix (Replies: 3)

  2. 2nd order to matrix (Replies: 12)

Loading...