Definition:Fundamental Matrix

Definition
A matrix function $\Phi(t)$ is a fundamental matrix of the system $x'=A(t)x$ if it solves the matrix system $X'=A(t)X$ and $\det \Phi(t)$ is nonvanishing.

Also see
See:
 * General Vector Solution of Fundamental Matrix
 * General Fundamental Matrix

for results concerning the general solution to such a system of equations.