  A mathematical framework is presented for use in the experimental
determination of the polarimetric response of observatory instrumentation.
Elementary principles of linear algebra are applied to model the full matrix
description of the polarization measurement equation by least-squares
estimation of non-linear, scalar parameters. The formalism is applied to
calibrate the center element of the Parkes Multibeam receiver using
observations of the millisecond pulsar, PSR J0437-4715, and the radio galaxy,
3C 218 (Hydra A).
