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 nonlinear, 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).
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