# Highly Nonlinear Approximations for Sparse Signal Representation

## Subspaces - Direct sum

A subset of a vector space is a subspace of if it is a vector space with respect to the vector space operations on . A subspace which is a proper subset of the whole space is called a proper subspace. Two subspaces and are complementary or disjoint if .

The sum of two subspaces and is the subspace of elements . If the subspaces and are complementary is called direct sum and indicated as . This implies that each element has a unique decomposition .

For the sets and , the set is denoted by .