- #1
brotherbobby
- 617
- 152
- Homework Statement
- The books says that "it is fairly easy" to verify the following product of two kronecker delta symbols : ##\epsilon_{ijk} \epsilon_{pqr} = \begin{vmatrix} \delta_{ip} & \delta_{iq} & \delta_{ir} \\ \delta_{jp} & \delta_{jq} & \delta_{jr} \\ \delta_{kp} & \delta_{kq} & \delta_{kr} \\ \end{vmatrix}##
- Relevant Equations
- We know the definition of the krokecker alternating symbol. Here all variables can only take values between 1 and 3. If any of the indices repeat, the value of the symbol is 0. If the indices alternate, the symbol takes on a minus sign.
I don't have a clue as to how to go about proving (or verifying) the equation above. It would be very hard to take individual values of i,j and k and p,q and r for each side and evaluate ##3^6## times! More than that, I'd like a proof more than a verification.
Any help would be welcome.
Any help would be welcome.