ABSTRACT
This chapter relates between dense and sparse matrices, since in numerical linear algebra the computations made with them needs to be faced in different ways and presents indeed different costs. Many of the matrix problems are in the form of systems of linear equations, although other matrix problems, such as eigenvalue calculations, can occur too. To reduce the number of stored indices, even if they need a relatively small space because they need just integer arrays, the Compressed Row Storage (CRS) and the Compressed Column Storage (CCS) are the most popular alternatives. In the CRS format, the consecutive nonzero entries of the matrix rows are put in contiguous memory locations. The matrix-vector product in CRS format is then obtained by means of the usual formula. In the standard CDS case, the matrix-vector product can be performed either by row or columns while the algorithm for the transpose product is just a minor variation of the latter.
