  We have previously defined synchronization (Gomez, E. and K. Schubert 2011)
as a relation between the times at which a pair of events can happen, and
introduced an algebra that covers all possible relations for such pairs. In
this work we introduce the synchronization matrix, to make it easier to
calculate the properties and results of $N$ event synchronizations, such as are
commonly encountered in parallel execution of multiple processes. The
synchronization matrix leads to the definition of N-event synchronization
algebras as specific extensions to the original algebra. We derive general
properties of such synchronization, and we are able to analyze effects of
synchronization on the phase space of parallel execution introduced in (Gomez E
Kai R, Schubert KE 2017)
