Einstein's summation notation

{
  "id": "MLC-T-MET-005295",
  "term": "Einstein's summation notation",
  "field": "Meteorology and atmospheric science",
  "definition": "A convention in mathematics and physics that simplifies the writing of sums over indices that appear exactly twice in a single term. When an index appears once as a subscript and once as a superscript, or twice as a subscript in a product, summation over that index is implied without explicitly writing the summation symbol. This notation is frequently used in tensor calculus and fluid dynamics equations to represent complex vector and tensor operations concisely.",
  "see_also": [
    "alternating unit tensor"
  ],
  "url": "https://mlchart.com/terminology/meteorology/einstein-s-summation-notation/"
}