  We review matrix methods as applied to tracer transport. Because tracer
transport is linear, matrix methods are an ideal fit for the problem. A
gridded, Eulerian tracer simulation can be approximated as a system of linear
ordinary differential equations (ODEs). The first-order stretching and
deformation of Lagrangian space can also be calculated using a system of linear
ODEs. Solutions to these equations are reviewed as well as special properties.
Using matrices to model Eulerian tracer transport can also help understand and
improve the stability of numerical solutions. Detailed derivations are
included.
