The Spectrum of a Linear Network: A Simple Approach to the n Compartment Problem

There are many instances in science where a set of linear differential equations with constant coefficients (a linear network) provides an adequate model with which to describe experimental data. A particularly common application in biology is to what is called 'compartment analysis'. It is well known that, except for some degenerate cases, the solution of the differential equations for one particular variable in the system has the form: