  The multiplicative and additive compounds of a matrix play an important role
in several fields of mathematics including geometry, multi-linear algebra,
combinatorics, and the analysis of nonlinear time-varying dynamical systems.
There is a growing interest in applications of these compounds, and their
generalizations, in systems and control theory. This tutorial paper provides a
gentle introduction to these topics with an emphasis on the geometric
interpretation of the compounds, and surveys some of their recent applications.
