Part 1. Matrices and linear dynamical systems
Chapter 1. Autonomous linear differential and difference equations
Chapter 2. Linear dynamical systems in Rd
Chapter 3. Chain transitivity for dynamical systems
Chapter 4. Linear systems in projective space
Chapter 5. Linear systems on Grassmannians

Part 2. Time-varying matrices and linear skew product systems
Chapter 6. Lyapunov exponents and linear skew product systems
Chapter 7. Periodic linear and differential and difference equations
Chapter 8. Morse decompositions of dynamical systems
Chapter 9. Topological linear flows
Chapter 10. Tools from ergodic theory
Chapter 11. Random linear dynamical systems

This book provides an introduction to the interplay between linear algebra and dynamical systems in continuous time and in discrete time. It first reviews the autonomous case for one matrix A via induced dynamical systems in Rd and on Grassmannian manifolds. Then the main nonautonomous approaches are presented for which the time dependency of A(t) is given via skew-product flows using periodicity, or topological (chain recurrence) or ergodic properties (invariant measures). The authors develop generalizations of (real parts of) eigenvalues and eigenspaces as a starting point for a linear algebra for classes of time-varying linear systems, namely periodic, random, and perturbed (or controlled) systems. --- summary provided by publisher