Projection operator
In
mathematics, a
projection operator on a
vector space is an
idempotent linear transformation. Such transformations
project any point in the vector space to a point in the subspace that is the image of the transformation. In an
inner product space, such an operator is an
orthogonal projection if and only if it is
self-adjoint. In finite-dimensional inner product spaces, an orthogonal projection matrix is one whose matrix
M satisfies
M2 =
M and
M ′ =
M where
M ′ is the
conjugate transpose of
M (see
projection (linear algebra)). The condition that
M ′ =
M says
M is a
symmetric matrix if all of the entries in
M are
real. In
physics, the term
projection operator usually means
self-adjoint projection operator.