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\section{Compressibility: finding a description of the problem}  The compressed-sensing approach presented in the previous section might seem to be applicable only to problems where the matrix to be calculated is sparse. However, this does not have to be the case. As matrices can be easily converted from one basis to another, an auxiliary basis, where the matrix to be reconstructed is expected to be sparse, can be used. Of course, the determination of such basis is specific for each problem and can go from trivial to quite complex. In general, finding the sparsifying basis has to do with the knowledge we have about the problem or what we expect about its solution.  Of course, the determination of a basis where the matrix is sparse depends on each problem and can go from trivial to quite complex. In general, finding the sparsifying basis has to do with the knowledge we have Using additional information  about the problemor what we expect about its solution. In fact, this type of information  is often used done  in numerical simulations. For example, in quantum chemistry is costumary customary  to represent the orbitals of a molecule in a basis formed by the orbitals of the atoms in the molecule. molecule~\cite{Szabo}, which allows for an efficient and compact representation and a controlled discretization error.  They often require the development of an ad-hoc theory  In the case of using a certain guess or approximation for compressed sensing, as the reconstruction is exact, even if the basis is not a good approximation we obtain the correct result. The penalty for a bad guess is additional computational cost. cost, which in the worst case is would be as costly as if compressed sensing was not used.  However, the properties of