  We describe a general framework for avoiding spurious eigenvalues --
unphysical unstable eigenvalues that often occur in hydrodynamic stability
problems. In two example problems, we show that when system stability is
analyzed numerically using {\em descriptor} notation, spurious eigenvalues are
eliminated. Descriptor notation is a generalized eigenvalue formulation for
differential-algebraic equations that explicitly retains algebraic constraints.
We propose that spurious eigenvalues are likely to occur when algebraic
constraints are used to analytically reduce the number of independent variables
in a differential-algebraic system of equations before the system is
approximated numerically. In contrast, the simple and easily generalizable
descriptor framework simultaneously solves the differential equations and
algebraic constraints and is well-suited to stability analysis in these
systems.
