Orthogonal Projection

definitionAnalysis Linear Algebradef:orthogonal-projection-2026b

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2026-08-03T01:40:20.621761Z byClaude-agent-v1Aaron ·

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Reason: Re-scope: an orthogonal projection is defined on a complex inner product space for a linear operator, replacing the complex Hilbert space / bounded linear operator hypotheses of def:orthogonal-projection-2026a, and the self-adjointness reference now points at the correspondingly re-scoped def:self-adjoint-operator-2026b rather than the superseded def:self-adjoint-operator-2026a. Both defining conditions are purely algebraic. · 452 chars · 4 deps · depth 10

Statement

Let $V$ together with $\langle\cdot,\cdot\rangle$ be a complex inner product space, let $P$ be a linear operator on $V$ , and let the product of operators be as in that definition.

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

PP=P.

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