The codes here implement core algorithms for linear algebra problems. The names often reflect the authorship of the central algorithm (Lanczos, Wiedemann, ...). In contrast, the "drivers" in the linbox/solutions directory are named for the problem solved (rank, det, ...). Those are generally wrappers of algorithms from this directory. Their purpose is to give a simple and direct user interface and sometimes to provide a solution strategy which is a hybrid of algorithms from this directory.
Algorithm classes and functions generally have the field class as a template parameter. Blackbox algorithms may have a BlackboxMatrix parameter or allow a Blackbox class as template parameter. Elimination codes work over DenseMatrix or SparseMatrix types with varying degrees of substitution among the types possible.