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Adjoint of a Linear Operator

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

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

The operator SS is an adjoint of TT if

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

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