The Levi-Civita symbol, often denoted as $\\epsilon_{ijk}$, is a mathematical object used in tensor calculus and differential geometry. It is a completely antisymmetric tensor that plays a crucial role in the computation of determinants and cross products, providing a way to encode orientation and volume in multi-dimensional spaces. This symbol helps relate the outer product of vectors to the determinant of matrices, emphasizing the geometric interpretation of these operations.
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