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

Homework Help: Determinant formula with einstein notation proof

  1. Sep 4, 2010 #1
    Hello, Im supposed to prove that the determinant of a second order tensor (a matrix) is equal to the following:

    det[A] = [tex] \frac{1}{6} \epsilon_{ijk} \epsilon_{pqr} A_{pi} A_{qj} A_{rk} [/tex]

    anyone have any idea how i would go about this? any method is welcome

    where the determinant of the matrix A is expressed below:

    det[A] =
    [tex] A_{11}(A_{23}A_{32}-A_{22}A_{33}) + A_{12}(A_{21}A_{33}-A_{23}A_{31}) + A_{13}(A_{22}A_{31}-A_{21}A_{32}) [/tex]
     
  2. jcsd
  3. Sep 5, 2010 #2

    HallsofIvy

    User Avatar
    Science Advisor

    Assuming that last formula is your definition of the determinant, then the obvious way to do this is to write out the actual sum implied by the first formula and show that the two formulas are the same thing.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook