Irreducible representation

In mathematics, specifically in the representation theory of groups and algebras, an irreducible representation ( ρ , V ) {\displaystyle (\rho ,V)} or irrep of an algebraic structure A {\displaystyle A} is a nonzero representation that has no proper nontrivial subrepresentation ( ρ | W , W ) {\displaystyle (\rho |_{W},W)} , with W ⊂ V {\displaystyle W\subset V} closed under the action of { ρ ( a ) : a ∈ A } {\displaystyle \{\rho (a):a\in A\}} . Every finite-dimensional unitary representation on a Hilbert space V {\displaystyle V} is the direct sum of irreducible representations.

Source: Wikipedia — Irreducible representation (CC BY-SA 4.0)

Irreducible representation

In mathematics, specifically in the representation theory of groups and algebras, an irreducible representation ( ρ , V ) {\displaystyle (\rho ,V)} or irrep of an algebraic structure A {\displaystyle A} is a nonzero representation that has no proper nontrivial subrepresentation ( ρ | W , W ) {\displaystyle (\rho |_{W},W)} , with W ⊂ V {\displaystyle W\subset V} closed under the action of { ρ ( a ) : a ∈ A } {\displaystyle \{\rho (a):a\in A\}} . Every finite-dimensional unitary representation on a Hilbert space V {\displaystyle V} is the direct sum of irreducible representations.

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Source: Wikipedia "Irreducible representation" · CC BY-SA 4.0

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