An open architecture software environment for handling sparse matrices and interchanging sparse matrix data is proposed. The proposed educational and research environment includes tools for the visualization of sparse matrices. A prototype implementation of these ideas called the Sparse Matrix Manipulation System is described. Two applications of these ideas are illustrated. The first application is to a comparative study of linear least squares methods, the second to the graphic description of the properties of partitioned sparse A−1 methods. The proposed system is built around three concepts: matrices, permutation vectors and partition vectors. Each concept is implemented as a stream of ASCII data. These streams are operated upon by filters (commands that accept data from standard input and direct output to standard output). Examples of commands include: permutations, addition of fills, factorization, computation of condition number and many others. Other commands generate sparse matrices and display topology maps and factorization path trees. This system permits interchanging information among programs written by different programmers, in different languages, possibly in different computers at different sites. The linear least squares example not only illustrates a practical use of the system, but underscores in a graphic manner the advantage of blocking algorithms to improve computational requirements and condition numbers in linear least squares problems. INFORMS Journal on Computing, ISSN 1091-9856, was published as ORSA Journal on Computing from 1989 to 1995 under ISSN 0899-1499.