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 ${\displaystyle x'=A(t)x+g(t)\,}$ where ${\displaystyle x\,}$ is a vector and ${\displaystyle A(t)\,}$ is an ${\displaystyle n\times n\,}$ matrix function of ${\displaystyle t\,}$, which is continuous for ${\displaystyle t\in I,a\leq t\leq b\,}$, where ${\displaystyle I\,}$ is some interval.

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