Summationskonvention
The Summationskonvention, often translated as the summation convention, is a notational shortcut used primarily in physics and engineering to simplify expressions involving sums. Introduced by Tullio Levi-Civita, it eliminates the need to explicitly write summation symbols. The convention states that whenever an index variable appears twice in a single term, once as a subscript and once as a superscript, it is implied that a summation is to be performed over all possible values of that index.
For example, in vector notation, the dot product of two vectors a and b in n-dimensional space
This convention is particularly useful in tensor calculus and differential geometry, where expressions can become very