##  [Alternation](/alternation) 

  ##  [Alternation](https://algebra.quantumdictionary.io/alternation-0) 

  

 [![Algebra](/sites/default/files/styles/large/public/2026-01/Algebra.png.webp?itok=3pHxBnUF)](/topic-specific-dictionaries/pure-mathematics/algebra)

- Pure Mathematics -

**Algebra Dictionary**

 







 

 

 

 



 

 

 

 

Definition

An operation on a multilinear tensor or form that projects onto its alternating (antisymmetric) part by taking the signed sum over permutations of arguments, producing an object that changes sign under odd permutations.