Final answer:
The contraction of the Levi-Civita symbol with the Kronecker delta is zero, which can be proved by considering the behavior of both symbols under permutation of indices and the identical nature of the Kronecker delta.
Step-by-step explanation:
The properties of the Levi-Civita symbol are fundamental in certain areas of mathematics and physics, particularly in vector calculus and tensor analysis. One property of interest is the contraction of the Levi-Civita symbol with the Kronecker delta, given by:
δijεijk = 0
This basically states that when you sum over repeated indices, the result is zero. This can be shown through the properties of the Levi-Civita symbol and the Kronecker delta. Since δij is the identity matrix and εijk is the Levi-Civita symbol, which changes sign depending on the permutation of its indices or is zero if any index is repeated, any contraction will result in summing terms that cancel each other out.