Let $A$ be a constant square matrix, $\Delta t$ is a scalar. I would imagine a taylor series of its exponential like this:
$$e ^{A\,\Delta t} = I + \sum_{n=1}^\infty \frac{(A\,\Delta t)^n}{n!} $$
Now if I want to approximate as a first order term only: $e ^{A\,\Delta t} = I + A\,\Delta t$, I have to say that $\frac{(A\,\Delta t)^2}{2!}$ should be small. But $A$ is not a number but a matrix. What matrix norm should I use to say that $\frac{(A\,\Delta t)^2}{2!}$ is small?