Let $n\in\mathbb N$. Let $M(n,\mathbb C)$ denote the complex [vector space](/page/Vector%20Space) of $n\times n$ complex matrices, and let $GL(n,\mathbb C)\subset M(n,\mathbb C)$ denote the group of invertible $n\times n$ complex matrices. Let
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\begin{align*}
\exp:M(n,\mathbb C)\to M(n,\mathbb C)
\end{align*}
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denote the matrix exponential map defined by the absolutely convergent [power series](/page/Power%20Series)