Definition:Fundamental Matrix

Definition
Let $\mathbf x' = \map A t \mathbf x$ be a system of $n$ linear first order ODEs.

Let $\map \Phi t$ be an $n \times n$ matrix function.

Then $\map \Phi t$ is a fundamental matrix of the system $\mathbf x' = \map A t \mathbf x$ :


 * it solves the matrix system $\mathbf X' = \map A t \mathbf X$
 * $\det \map \Phi t$ is nonvanishing.

Also see

 * General Vector Solution of Fundamental Matrix
 * General Fundamental Matrix