Definition:Complementary Idempotent

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 $H$.

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