  We discuss the (right) eigenvalue equation for $\mathbb{H}$, $\mathbb{C}$ and
$\mathbb{R}$ linear quaternionic operators. The possibility to introduce an
isomorphism between these operators and real/complex matrices allows to
translate the quaternionic problem into an {\em equivalent} real or complex
counterpart. Interesting applications are found in solving differential
equations within quaternionic formulations of quantum mechanics.
