The recent result obtained by Givens and Kostinski [J. Mod. Opt. 40, 471 (1993)] successfully solves the old and important problem in polarization optics of characterizing a given 4×4 matrix as a Mueller matrix from a mathematical point of view. For practical purposes, however, a further elaboration on this result is needed, namely, the problem of characterizing a matrix whose elements have been empirically obtained after the measurement of a given number of independent quantities that are affected by errors. We solve this problem by first obtaining an alternative form of the Givens–Kostinski theorem that allows us to figure out an algorithm for calculating the error propagation. It turns out that the experimental matrix can be finally regarded as physically meaningful or not, or even undecidable, depending on such errors. As a tool for potential users, a routine (in both FORTRAN and IDL languages) that carries out all the numerical calculations is available via ftp at a specified address.