  We discuss the solution of eigenvalue problems associated with partial
differential equations that can be written in the generalized form
$\m{A}x=\lambda\m{B}x$, where the matrices $\m{A}$ and/or $\m{B}$ may depend on
a scalar parameter. Parameter dependent matrices occur frequently when
stabilized formulations are used for the numerical approximation of partial
differential equations. With the help of classical numerical examples we show
that the presence of one (or both) parameters can produce unexpected results.
