Eigenvalues and Singular Values

Abstract

So far, our physical applications of linear algebra have concentrated on statics: unchanging equilibrium configurations of mass–spring chains, circuits, and structures, all modeled by linear systems of algebraic equations. It is now time to set the universe in motion. In general, a (continuous) dynamical system refers to the (differential) equations governing the time-varying motion of a physical system, be it mechanical, electrical, chemical, fluid, thermodynamical, biological, financial, . . . . Our immediate goal is to solve the simplest class of continuous dynamical models, which are first order autonomous linear systems of ordinary differential equations.