probability theory and ergodic theory, the invariant sigma-algebra is a sigma-algebra formed by sets which are invariant under a group action or dynamical system...

the map T {\displaystyle T} is measurable, invariant sets form a sigma-algebra, the invariant sigma-algebra. The notion of invariance is formalized in...

{\displaystyle (X,\Sigma )} is said to be invariant under f {\displaystyle f} if, for every measurable set A {\displaystyle A} in Σ , {\displaystyle \Sigma ,} μ (...

K_{j}\right]&=-i\hbar \epsilon _{ijk}L_{k}\end{aligned}}} The Casimir invariants of this algebra are P μ P μ {\textstyle P_{\mu }P^{\mu }} and W μ W μ {\textstyle...

otherwise, a kind of invariant delta function on isomorphism classes of intervals. Its powers in the incidence algebra are the other invariant delta functions...

v_{n}\mapsto v_{\sigma (1)}\otimes \cdots \otimes v_{\sigma (n)}} defines a linear endomorphism of Tn(V). A symmetric tensor is a tensor that is invariant under...

viewpoint, the universal enveloping algebra of the Lie algebra of a Lie group may be identified with the algebra of left-invariant differential operators on the...

mathematics, a Clifford algebra is an algebra generated by a vector space with a quadratic form, and is a unital associative algebra with the additional structure...

which provides a convenient alternative to the left-invariant vector field for calculating the Lie algebra. We can write down a set of six generators: Vector...

In linear algebra and functional analysis, a projection is a linear transformation P {\displaystyle P} from a vector space to itself (an endomorphism)...