In mathematics, a self-adjoint operator on a complex vector space V {\displaystyle V} with inner product ⟨ ⋅ , ⋅ ⟩ {\displaystyle \langle \cdot ,\cdot \rangle } is a linear map A {\displaystyle A} (from V {\displaystyle V} to itself) that is its own adjoint. That is, ⟨ A x , y ⟩ = ⟨ x , A y ⟩ {\displaystyle \langle Ax,y\rangle =\langle x,Ay\rangle } for all x , y ∈ V {\displaystyle x,y\in V} .
In mathematics, a self-adjoint operator on a complex vector space V {\displaystyle V} with inner product ⟨ ⋅ , ⋅ ⟩ {\displaystyle \langle \cdot ,\cdot \rangle } is a linear map A {\displaystyle A} (from V {\displaystyle V} to itself) that is its own adjoint. That is, ⟨ A x , y ⟩ = ⟨ x , A y ⟩ {\displaystyle \langle Ax,y\rangle =\langle x,Ay\rangle } for all x , y ∈ V {\displaystyle x,y\in V} .
Source: Wikipedia "Self-adjoint operator" · CC BY-SA 4.0
Share this article: X · Bluesky