Definition:Complementary Idempotent

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Definition

Let $\HH$ be a Hilbert space.

Let $A$ be an idempotent operator on $\HH$.


Then the complementary idempotent (operator) of $A$ is the bounded linear operator $I - A$, where $I$ is the identity operator on $H$.


Complementary Projection

Let $A$ be a projection on $\HH$.


Then the complementary projection (operator) of $A$ is the bounded linear operator $I - A$, where $I$ is the identity operator on $\HH$.


Also see