  A unification of characteristic mode decomposition for all method-of-moment
formulations of field integral equations describing free-space scattering is
derived. The work is based on an algebraic link between impedance and
transition matrices, the latter of which was used in early definitions of
characteristic modes and is uniquely defined for all scattering scenarios. This
also makes it possible to extend the known application domain of characteristic
mode decomposition to any other frequency-domain solver capable of generating
transition matrices, such as finite difference or finite element methods. The
formulation of characteristic modes using a transition matrix allows for the
decomposition of induced currents and scattered fields from arbitrarily shaped
objects, providing high numerical dynamics and increased stability, removing
the issue of spurious modes, and offering good control of convergence. This
first part of a two-part paper introduces the entire theory, extensively
discusses its properties and offers its basic numerical validation.
