The Matrix is an interconnected network of roles, case, syntax, and phonics reflecting historic human activity taking place in any given semantic frame of reference. Each Frame, with its unity of objectives, domain, community and work, delimits a subnetwork of connections between those matrix points involved and the specific human population and activity itself in the course of its development.
The ideal language learning Syllabus would be a progression of semantically driven Frames organized as proximal zones of development in the learner's specific adquisition of that language.
Given that the Matrix constitutes 100% language competence, it could also be used as an evaluation tool, but care would have to be taken for that to not be too mechanical or opinionated.
But we certainly have an ideal Tracker, which would reflect the specific path of issues generated by the passage of each learner through the Frames, a history of all their connections and experience on the Matrix itself, and so an objectivization of communicative competence in actual practice at any given point in time.
So the Matrix is a Syllabus, or learning framework (actually a set of Frames!), a Tracker; but is nothing without being a Network also in the sense of community. A community Network may be organized around the population of learners working with a given Frame. This may be by chance (you can find others working on the same Frame) or a group of Learners may choose to adopt a given Syllabus in conjunction with a tasks and activities organized by Tutors and made available by Coaches.
So the Matrix is a Network many times over, not only as a the set of networked components of any given Frame, and as the population instantiating the case roles in the development of an activity involving the Frame, but also in the Network of Tutors, Coaches and Learners working in the Course of a Syllabus.
Note: The term Grid was originally used instead of Matrix prior to 2014, although competence was used as early as 1983 via critical readings of Chomsky. Replaced with Matrix for the sake of continuity with the current, less mechanical and more powerful terminology.