The status functions method for processing and interpretation of the measurement data of interactions in the educational environment

We propose a mathematical method based on the use of complex functions as a status attributed to the state of the object functions. The method is focused on the direct de-scription of the mathematical model of the feedback channel of ergatic systems. Status functions are formed as an optimal, orthonormal basis of the system. The rules for working with the status functions are introduced, and their interpretation is proposed. A method for forming the operator for conversing signals given as status functions is proposed. Thus, the mathematical support of an analysis of the interaction in the integrated educational environment is improved on the basis of modelling competence portraits of participants of the learning process, which is characterized by the use of status functions. This allowed for the multicomponent assessment of competence in the form of complex-valued functions.