Definition:Complementary Projection

Definition
Let $\HH$ be a Hilbert space. 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 Projection is Projection
 * Complementary Projection of Complementary Projection is Projection for justification of the name for $I - A$
 * Definition:Complementary Idempotent
 * Complementary Projection is Complementary Idempotent