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Hello, I am 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]
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]