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Matrix exponential

For a square matrix

A

, its exponential is the convergent power series

e^{t A} = \sum_{k = 0}^{\infty} \frac{t ^{k} A ^{k}}{k !} .

It is the fundamental matrix for

y^{'} = A y

and satisfies

e^{(s + t) A} = e^{s A} e^{t A}

.

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- Laplace transform of a matrix exponential Matrix exponential 22

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