I am trying to understand the matrix measured proposed by W. Coppel in "Stability and Asymptotic Behavior of Differential Equations" in 1965, but I cannot find a pdf of this paper online, so if anyone can help me find this, that would be awesome. These are the main questions:
Let $A \in \mathbb{R}^{n\times n}$. Define $$\mu(A) = \lim_{\epsilon \rightarrow 0^+} \frac{||\mathbb{1} + \epsilon A|| - 1}{\epsilon}$$ Where $\mathbb{1}$ denotes the identity matrix.
Show that: $$||e^{At}|| \le e^{\mu(A)t}$$
Could someone please point me in the right direction? Thank you.