2022/04/01 by Eyal Bar-Shalom, Bar-Shalom, Eyal, Omri Dalin +3 · 1 citation
Computer Science · Engineering · Physics and Astronomy · #Control and Stability of Dynamical Systems #FOS: Mathematics #Matrix Theory and Algorithms #Optimization and Control (math.OC) #Quantum chaos and dynamical systems
paper · pdf · doi:10.48550/arxiv.2204.00676
openalex publication_date 2022/04/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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. The goal of this tutorial paper is to provide a gentle and self-contained introduction to these topics with an emphasis on the geometric interpretation of the compounds, and to describe some of their recent applications including several non-trivial generalizations of positive systems, cooperative systems, contracting systems, and more.