The Jacobson radical of a matrix algebra A is the set of matrices b in A such that tr(ab) = 0 for all a in A.  The Jacobson radical consists entirely of nilpotent matrices and coincides with the nilradical of A.

A list of matrices defining a basis for the Jacobson radical is returned.  If the Jacobson radical is trivial, then an empty list is returned.

The command JacobsonRadical is part of the DifferentialGeometry:-LieAlgebras package.  It can be used in the form JacobsonRadical(...) only after executing the commands with(DifferentialGeometry) and with(LieAlgebras), but can always be used by executing DifferentialGeometry:-LieAlgebras:-JacobsonRadical(...).