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For a square matrix $A$, its exponential is the convergent power series
$$
e^{tA}=\sum_{k=0}^{\infty}\frac{t^kA^k}{k!}.
$$
It is the fundamental matrix for $y'=Ay$ and satisfies $e^{(s+t)A}=e^{sA}e^{tA}$.


Matrix exponential

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