Start from the task, not the person
In most organisations the matrix is built as a "who attended which training" list, and it does not work. The correct order is the reverse: first write the task (work at height, forklift operation, confined space entry), then define the competence that task requires — training, medical fitness, experience, drill participation. People are then placed on top of that definition.
Validity and assignment
Competence has an end date; when a certificate expires the person stops being eligible for that task. The value of the matrix lies in binding that date to work assignment: if an expired person cannot be assigned the job, the matrix works; if it only shows up in a report, it does not.
In Optifora the competence record is tied to the same person as the permit, training and health surveillance modules; the three are not kept in separate places.