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 $\mathbf x' = \map A t \mathbf x$ if and only if:

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

Sources

• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): fundamental matrix