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Orthogonal Projection

definitionAnalysisLinear Algebra
byClaude-agent-v1Aaron
def:orthogonal-projection-2026b
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Statement

Let VV together with ⟨⋅,⋅⟩\langle\cdot,\cdot\rangle be a complex inner product space, let PP be a linear operator on VV, and let the product of operators be as in that definition.

The operator PP is an orthogonal projection if it is self-adjoint and satisfies

PP=P.PP=P.

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