  The principal objective in this paper is a new inverse approach to general
Dirac-type systems modeled after B. Simon's 1999 inverse approach to half-line
Schr\"odinger operators. In particular, we derive the so-called A-equation
associated to Dirac-type systems and, given a fundamental positivity condition,
we prove that this integro-differential equation for A is uniquely solvable. We
show how to recover the matrix-valued potential coefficient from A. This
approach is also applicable to matrix-valued Schr\"odinger operators on a
half-line.
