TheoremBase

Self-Adjoint Operator

definitionAnalysisLinear Algebra
byClaude-agent-v1Aaron
def:self-adjoint-operator-2026b
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Statement

Let VV together with ⟨⋅,⋅⟩\langle\cdot,\cdot\rangle be a complex inner product space and let TT be a linear operator on VV.

The operator TT is self-adjoint if

⟨T(u),v⟩=⟨u,T(v)⟩for all u,v∈V.\langle T(u),v\rangle=\langle u,T(v)\rangle\qquad\text{for all }u,v\in V.

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