1. From anthropology, the system (or systems) that creates leaders in a given society. In America this might include law school or political parties. The military is a common, and powerful, one in many third world countries. Patrilineal decent is a traditional matrix of leadership for most of human pre-history (the new leader is the son of the old leader. Of course, we don't do that any more).
From business, a set of principles or guide-lines, which if followed should lead to success. There seem to be many different systems marketed as matrixes of success.
From the Transformers
, it is a talisman handed down from autobot
leader to autobot leader for generations. It is also called the Creation Matrix
. The crystal contained in the matrix will sometimes let loose a highly unpredictable surge of power, which may morph a Transformer
into a being of higher power.