# Highly Nonlinear Approximations for Sparse Signal Representation

## Inner product space

An **inner product** on a vector space is a map from
to
which
satisfies the following axioms

- , and
- and .
- .

**inner product space**.

An **inner product** on a vector space is a map from
to
which
satisfies the following axioms

- , and
- and .
- .