  Bleher and Kuijlaars recently showed that the eigenvalue correlations from
matrix ensembles with external source can be expressed by means of a kernel
built out of special multiple orthogonal polynomials. We derive a
Christoffel-Darboux formula for this kernel for general multiple orthogonal
polynomials. In addition, we show that the formula can be written in terms of
the solution of the Riemann-Hilbert problem for multiple orthogonal
polynomials, which will be useful for asymptotic analysis.
