ABSTRACT
The classical theory of measurement is built upon the conception of an interaction between the system of interest and the measuring apparatus that can be made arbitrarily small, or at least precisely compensated, so that one can speak meaningfully of an idealized measurement that disturbs no property of the system. In the most elementary type of measurement, an ensemble of independent similar systems is sorted by the apparatus into subensembles, distinguished by definite values of the physical quantity being measured. The use of complex numbers in the measurement algebra implies the existence of a dual algebra in which all numbers are replaced, by the complex conjugate numbers. No physical result can depend upon which algebra is employed. The measurement symbols of a given description provide a basis for the representation of an arbitrary operator by N2 numbers, and the abstract properties of operators are realized by the combinatorial laws of these arrays of numbers, which are those of matrices.
