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Given a $n \times n$ matrix $A$ over the complex numbers, the exponential of $A$ is defined as $$\exp(A) := \sum_{k = 1}^\infty \frac1{k!} A^k , \qquad \tag{$\star$}\label{468645_star}$$ where ...

Wikipedia states in the exponential map section about the exponential of a matrix that for any matrices $X$, $Y$ it holds that $\|e^{X+Y}-e^{X}\| \leq \|Y\|e^{\|X\|} e^{\|Y\|}$ where $\|\cdot\|$ ...