Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Tensor problem

  1. Nov 6, 2009 #1
    Excercise Exercise 1.6 of Roger Blandford and Kip Thorne's online textbook Applications of Classical Physics:

    "In Minkowski spacetime, in some inertial reference frame, the vector A and second rank
    tensor T have as their only nonzero components A0 = 1, A1 = 2, A2 = A3 = 0. T00 = 3, T01 = T10 = 2, T11 = −1. Evaluate T(A, A) and the components of T(A,__) and A[tex]\otimes[/tex]T."

    http://www.pma.caltech.edu/Courses/ph136/yr2008/

    The given answers to the first two questions are T(A, A) = -9, and T(A,__) = (1, -4, 0, 0). But I get 7, and (7, 0, 0, 0).

    [tex]\left( \begin{matrix} 1 & 2 & 0 & 0 \end{matrix} \right) \left(\begin{matrix} 3 & 2 & 0 & 0 \\ 2 & -1 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \end{matrix} \right) = \left( \begin{matrix} 7 & 0 & 0 & 0 \end{matrix} \right)[/tex]

    [tex]\left( \begin{matrix} 7 & 0 & 0 & 0 \end{matrix} \right) \left( \begin{matrix} 1 \\ 2 \\ 0 \\ 0 \end{matrix} \right) = 7[/tex]
     
  2. jcsd
  3. Nov 6, 2009 #2
    You forgot to lower the indices of A before doing the multiplication.
     
  4. Nov 7, 2009 #3
    Thanks! Yes, that's better:

    [tex]\left( \begin{matrix} -1 & 2 & 0 & 0 \end{matrix} \right) \left(\begin{matrix} 3 & 2 & 0 & 0 \\ 2 & -1 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \end{matrix} \right) = \left( \begin{matrix} 1 & -4 & 0 & 0 \end{matrix} \right)[/tex]

    [tex]\left( \begin{matrix} 1 & -4 & 0 & 0 \end{matrix} \right) \left( \begin{matrix} -1 \\ 2 \\ 0 \\ 0 \end{matrix} \right) = -9[/tex]
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Tensor problem
  1. Tensors and Tensors (Replies: 7)

  2. Ricci tensor problem (Replies: 16)

Loading...