Linear algebraic theory of partial coherence: discrete fields and measures of partial coherence

We present a linear algebraic theory of partial coherence which allows precise mathematical definitions of concepts such as coherence and incoherence. This not only provides new perspectives and insights, but also allows us to employ the tools of linear algebra in applications. We define a scalar measure of the degree of partial coherence of an optical field which is zero for complete incoherence and unity for full coherence.