The Levi-Civita symbol, denoted as $$\epsilon_{ijk}$$, is a mathematical construct used to represent the orientation of a coordinate system in three-dimensional space. It takes the value of +1 for even permutations of its indices, -1 for odd permutations, and 0 if any two indices are equal. This symbol is crucial for defining operations like the cross product and plays a significant role in various tensor calculus operations, connecting to concepts such as mixed tensors, symmetry properties, and tensor representation through index notation.
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