A new perspective on transcripts by means of their matrix representation

Transcripts map the ordinal pattern representation of e.g. one time series onto another (coupled) one by carrying out permutations. Their representation in terms of permutation matrices motivates the use of elements of linear algebra to derive properties that are of interest for the characterization of coupled dynamical systems. In this contribution, we summarize a number of these properties from a theoretical point of view, in particular those resulting from the application of algebraic techniques, such as eigenvalue calculations, to averaged transition matrices. Finally, we test this approach on data from mathematical models of coupled systems and on a real world data set.