Ordinary Differential Equations and Dynamical Systems Vol2 · Problem 2.1

Existence Theory

Mathematics — Calculus · matrix-exponential

Problem

Find

\exp At

for the following matrices. (Suggestion: Use the definition of exp.) (a)

A = \begin{bmatrix} \mu & \omega \\ \omega & \mu \end{bmatrix}

(b)

A = \begin{bmatrix} \mu & \omega \\ -\omega & \mu \end{bmatrix}

(c)

A = \begin{bmatrix} \mu & \omega & 1 & 0 \\ -\omega & \mu & 0 & 1 \\ 0 & 0 & \mu & \omega \\ 0 & 0 & -\omega & \mu \end{bmatrix}