  The principal results of this paper consist of an intrinsic definition of the
Evans function in terms of newly introduced generalized matrix-valued Jost
solutions for general first-order matrix-valued differential equations on the
real line, and a proof of the fact that the Evans function, a
finite-dimensional determinant by construction, coincides with a modified
Fredholm determinant associated with a Birman-Schwinger-type integral operator
up to a nonvanishing factor.
