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fundamental matrix

A matrix whose columns are n linearly independent solutions of a system.

A fundamental matrix $\Phi(t)$ of $\mathbf{x}'=A\mathbf{x}$ has as its columns $n$ linearly independent solutions; the general solution is $\mathbf{x}(t)=\Phi(t)\mathbf{c}$ for a constant vector $\mathbf{c}$ .