Definition of Anticommutativity. Meaning of Anticommutativity. Synonyms of Anticommutativity

Here you will find one or more explanations in English for the word Anticommutativity. Also in the bottom left of the page several parts of wikipedia pages related to the word Anticommutativity and, of course, Anticommutativity synonyms and on the right images related to the word Anticommutativity.

Definition of Anticommutativity

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Meaning of Anticommutativity from wikipedia

- In mathematics, anticommutativity is a specific property of some non-commutative mathematical operations. Swapping the position of two arguments of an...
- (−1)deg(x)deg(y)yx for all nonzero homogeneous elements x and y (i.e. it is an anticommutative algebra) and has the further property that x2 = 0 (nilpotence) for...
- (even) or 1 (odd). Some graded rings (or algebras) are endowed with an anticommutative structure. This notion requires a homomorphism of the monoid of the...
- degree one component) always contains nilpotent elements. A Z-graded anticommutative algebra with the property that x2 = 0 for every element x of odd grade...
- mnemonic applies also to many formulas given in this article. The anticommutativity of the cross product, implies that j × i = − k k × j = − i i × k =...
- {\displaystyle [A,[B,C]]+[B,[C,A]]+[C,[A,B]]=0} Relation (3) is called anticommutativity, while (4) is the Jacobi identity. [ A , B C ] = [ A , B ] C + B [...
- is anticommutative and not ****ociative. The cross product also satisfies the Jacobi identity. Lie algebras are algebras satisfying anticommutativity and...
- properties follow from the definition, including the following identities: Anticommutativity: x × y = − y × x {\displaystyle \mathbf {x} \times \mathbf {y} =-\mathbf...
- i ) × Δ r i ) + ( ω × Δ r i ) × − ( ω × Δ r i ) …  cross-product anticommutativity = Δ r i × ( ω × ( ω × Δ r i ) ) + ω × ( ( ω × Δ r i ) × Δ r i ) +...
- second one. Subtraction follows several important patterns. It is anticommutative, meaning that changing the order changes the sign of the answer. It...