# Highly Nonlinear Approximations for Sparse Signal Representation

## Oblique and Orthogonal Projector

When
happens to be equal to
, which indicates the
orthogonal complement of
,
the projector is called **orthogonal projector**
onto
.
This is the case if and only if the projector is *self adjoint*.

A projector which is not orthogonal is called an **oblique
projector** and we need two subscripts to represent it. One subscript to
indicate the range of the projector and another to represent the
subspace along which the projection is performed.
Hence the projector onto along
is indicated as
.

The particular case
corresponds to an *orthogonal projector*
and we use the special notation
to indicate such a
projector.
When a projector onto is used for signal processing,
can be chosen according
to the processing task. The examples below illustrate
two different situations.

**Subsections**