In mathematics, the commutator gives an indication of the extent to which a certain binary operation fails to be commutative. There are different definitions...

In mathematics, more specifically in abstract algebra, the commutator subgroup or derived subgroup of a group is the subgroup generated by all the commutators...

used to denote the commutator. In group theory, the commutator [g,h] is commonly defined as g−1h−1gh. In ring theory, the commutator [a,b] is defined as...

A mathematical symbol is a figure or a combination of figures that is used to represent a mathematical object, an action on mathematical objects, a relation...

and commutator, describe the extent to which a given group is not abelian. Symmetry groups are groups consisting of symmetries of given mathematical objects...

In mathematical physics, the ternary commutator is an additional ternary operation on a triple system defined by [ a , b , c ] = a b c − a c b − b a c...

In mathematics, more specifically in group theory, a group is said to be perfect if it equals its own commutator subgroup, or equivalently, if the group...

In mathematics, the commutator subspace of a two-sided ideal of bounded linear operators on a separable Hilbert space is the linear subspace spanned by...

In mathematics, a binary operation is commutative if changing the order of the operands does not change the result. It is a fundamental property of many...

In mathematics, rings are algebraic structures that generalize fields: multiplication need not be commutative and multiplicative inverses need not exist...

L_{x},\;\;\left[L_{z},L_{x}\right]=i\hbar L_{y},} where [ , ] denotes the commutator [ X , Y ] ≡ X Y − Y X . {\displaystyle [X,Y]\equiv XY-YX.} This can be...

Schrödinger picture respectively, H is the Hamiltonian and [·,·] denotes the commutator of two operators (in this case H and A). Taking expectation values automatically...

mathematics, the commutator collecting process is a method for writing an element of a group as a product of generators and their higher commutators arranged...

corresponds exactly to the commutator product in geometric algebra and both use the same symbol × {\displaystyle \times } . The commutator product is defined...

derivation in abstract algebra. If the algebra A is noncommutative, then the commutator with respect to an element of the algebra A defines a linear endomorphism...

Poisson brackets. In quantum mechanics, it is satisfied by operator commutators on a Hilbert space and equivalently in the phase space formulation of...

In mathematics, a module is a generalization of the notion of vector space in which the field of scalars is replaced by a (not necessarily commutative)...

In mathematics, E8 is any of several closely related exceptional simple Lie groups, linear algebraic groups or Lie algebras of dimension 248; the same...

decisions. Brackets are used in mathematics in a variety of notations, including standard notations for commutators, the floor function, the Lie bracket...

similar to the commutator of any pair of matrices. Conversely, any square matrix with zero trace is a linear combination of the commutators of pairs of matrices...

The mathematical formulations of quantum mechanics are those mathematical formalisms that permit a rigorous description of quantum mechanics. This mathematical...

{\displaystyle \textstyle \prod _{i=1}^{n}h_{i}} in H/H′, where H′ is the commutator subgroup of H. The order of the factors is irrelevant since H/H′ is abelian...

In the mathematical field of differential topology, the Lie bracket of vector fields, also known as the Jacobi–Lie bracket or the commutator of vector...

interior product defined above and it is clear whether [·,·] denotes the commutator or the Lie bracket of vector fields. Various generalizations of the Lie...

In mathematics, the term homology, originally introduced in algebraic topology, has three primary, closely-related usages. The most direct usage of the...

group homomorphisms as morphisms Metabelian group, a group where the commutator subgroup is abelian Abelianisation Abelian variety, a complex torus that...

center of E and [ , ] denotes the commutator. Equivalently, a group is quasisimple if it is equal to its commutator subgroup and its inner automorphism...

point particle in one dimension, where [x , px] = x px − px x is the commutator of x and px , i is the imaginary unit, and ℏ is the reduced Planck constant...

convergent) in X {\displaystyle X} and Y {\displaystyle Y} and iterated commutators thereof. The first few terms of this series are: Z = X + Y + 1 2 [ X...

commutators vanish. However, for fermions the mathematics is different, involving anticommutators instead of commutators. In the context of the quantum harmonic...