  The typical definition of the characteristic polynomial seems totally ad hoc
to me. This note gives a canonical construction of the characteristic
polynomial as the minimal polynomial of a "generic" matrix. This approach works
not just for matrices but also for a very broad class of algebras including the
quaternions, all central simple algebras, and Jordan algebras.
  The main idea of this paper dates back to the late 1800s. (In particular, it
is not due to the author.) This note is intended for a broad audience; the only
background required is one year of graduate algebra.
