A mathematical operator (typically a binary operator, represented by *) is anticommutative if and only if it is true that

x * y = −(y * x)

for all x and y on the operator's valid domain (e.g. R for subtraction, and R³ vectors for cross products).

Examples of the use of anticommutative operators include:

• Subtraction
• Cross products
• Lie algebras
• Lie rings

See also

• Commutativity
• Symmetry in mathematics

Abstract algebra | Binary operations | Anticommutativité | Антикоммутативность | 反交換律