USE OF VECTOR ALGEBRA TO ENSURE THE INTEGRITY OF THE COMPONENTS OF THE PROJECT-VECTOR MANAGEMENT MULTISYSTEM OF EDUCATIONAL ENVIRONMENTS

The article is devoted to the development of a mathematical model of the projectvector space of educational environments. Mathematical formalization of the project-vector space is performed. The main directions of application of vector algebra to ensure the integrity of the components of multisystem of project-vector management of educational environments are proposed. It is shown that in order to build an effective project management system, it is not so much the direction of movement of individual objects that is important, but the same or different vectors of their movement in the project-vector space. The same vectors mean that the movement of objects of different projects is equally conditioned. A model for calculating the distances between vectors and determining the optimal set of project groups (respectively, subsystems of the project management system) is proposed. Mathematical models have been developed for estimating the magnitude of the similarity of vectors over significant time intervals, as well as estimating the magnitude of the proximity of vectors specified by qualitative categories. These models show that the slower the objects of various projects move relative to each other, the more profitable it is to attribute them to one group and manage them on the basis of a single component of a multi-project management system.