Linear maps of modules with coefficients in a principal ideal domain #
Since a submodule of a free module over a PID is free, certain constructions which are often developed only for vector spaces may be generalised to any module with coefficients in a PID.
This file is a location for such results and exists to avoid making large parts of the linear algebra import hierarchy have to depend on the theory of PIDs.
Main results: #
If a linear endomorphism of a (finite, free) module
M takes values in a submodule
p ⊆ M,
then the trace of its restriction to
p is equal to its trace on