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Self-adjoint operator
Linear operator equal to its own adjoint
Self-adjoint operator
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} . If V {\displaystyle V} is finite-dimensional with a given orthonormal basis, this is equivalent to the condition that the matrix of...
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