Author: Martin Maechler, ETH Zurich Title: Class Hierarchies and Method Organization for Matrices Abstract: In co-developing the R package "Matrix", we have used S4 classes and methods throughout. Using class hierarchies based on three (sometimes even four) different property classes was found to be powerful. Since many methods apply to \emph{pairs} of matrices, we have defined many methods for high level (virtual) classes rather than for many or all (pairs of) 47 ``actual'' (non-virtual) classes. Using the example of "Matrix", we show tools and draw conclusions for more general class and method management using S4, including inheritance visualization and organization of testing code.