# Math Help - Find a nonhyperbolic matrix which satisfies certain conditions

1. ## Find a nonhyperbolic matrix which satisfies certain conditions

For $e^{At} = 1/2\begin{bmatrix}e^{2t}+e^{-t} & e^{2t} - e^{-t} \\ e^{2t}-e^{-t} & e^{2t}+e^{-t}\end{bmatrix}$ for all t $\in$ $\mathbb{R}$. how to find A?

2. ## Re: Find a nonhyperbolic matrix which satisfies certain conditions

If you let $\vec{x} = e^{At}$, the $\vec{x}$ would satisfy the ODE $\dfrac{d\vec{x}}{dt} = A \vec{x}$.