Alternating unit tensor

{
  "id": "MLC-T-MET-003460",
  "term": "Alternating unit tensor",
  "field": "Meteorology and atmospheric science",
  "definition": "A mathematical object, also called the Levi-Civita symbol, used to simplify vector and tensor calculations in three-dimensional space. Its components are defined as +1 for an even permutation of its indices, -1 for an odd permutation, and 0 if any two indices are repeated. In atmospheric dynamics, it provides a compact notation for the vector cross product and the curl operator, which are found in the equations for vorticity and momentum.",
  "url": "https://mlchart.com/terminology/meteorology/alternating-unit-tensor/"
}