What is the name of this operator?

Question

I was using a projection algorithm and came across and operator $$[~]_{+}$$, can anyone tell me what is this operator called and what it represents?

Answer 1

Sometimes $[a,b]_{+}$ is used to denote the anticommutator of two elements a and b, while $[a,b]_{-}$ is then used for the commutator.

The commutator of two elements a and b of a ring (or any associative algebra) is defined by

$\{a,b\}=ab-ba=[a,b]_{-}$.

The anticommutator of two elements a and b of a ring or associative algebra is defined by

$\{a,b\}=ab+ba=[a,b]_{+}$.

The anticommutator can be used to define Clifford algebras and Jordan algebras, or in the derivation of the Dirac equation in particle physics.