Definition:Fundamental Matrix
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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
Sources
- 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): fundamental matrix