# Highly Nonlinear Approximations for Sparse Signal Representation

## Orthogonality

Two vectors and in an inner product space are said to be
**orthogonal** if
If, in addition,
they are **orthonormal**.

Two subspaces
and
are orthogonal if
for all
and
.
The sum of two orthogonal subspaces
and
is
termed **orthogonal sum** and will be indicated as
The subspace
is called the
**orthogonal complement** of
in . Equivalently,
is the orthogonal complement of
in .