  The dynamics of the eigenvalues (semimartingales) of a L\'{e}vy process $X$
with values in Hermitian matrices is described in terms of It\^{o} stochastic
differential equations with jumps. This generalizes the well known
Dyson-Brownian motion. The simultaneity of the jumps of the eigenvalues of $X$
is also studied. If $X$ has a jump at time $t$ two different situations are
considered, depending on the commutativity of $X(t)$ and $X(t-)$. In the
commutative case all the eigenvalues jump at time $t$ only when the jump of $X$
is of full rank. In the noncommutative case, $X$ jumps at time $t$ if and only
if all the eigenvalues jump at that time when the jump of $X$ is of rank one.
