Green's matrix

In mathematics, and in particular ordinary differential equations, a Green's matrix helps to determine a particular solution to a first-order inhomogeneous linear system of ODEs. The concept is named after George Green. For instance, consider where is a vector and is an matrix function of , which is continuous for , where is some interval. Now let be linearly independent solutions to the homogeneous equation and arrange them in columns to form a fundamental matrix: Now is an matrix solution of .