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
- Complementary Idempotent is Idempotent
- Complementary Idempotent of Complementary Idempotent is Idempotent for justification of the name for $I - A$
- Range of Idempotent is Kernel of Complementary Idempotent