The analysis of generalized eigenvalue problems is central to understanding a number of complex phenomena, including the stability of nonlinear waves. One generally seeks a characterization of a linearized spectrum in relation to the complex plane (e.g., eigenvalues strictly in the right half plane) from which one can deduce the stability of the system and the presence of features such as bifurcations of Hamiltonian--Hopf type. Two fundamentally different but useful tools for analyzing spectral stability include the Krein signature and the Evans function. The Krein signature is helpful in investigating the stability of purely imaginary eigenvalues (i.e., whether eigenvalues will move toward the right half plane under perturbations), while the Evans function can be used to detect eigenvalue locations. The paper "Graphical Krein Signature Theory and Evans--Krein Functions," by Richard Kollar and Peter Miller, highlights a graphical interpretation of the Krein signature and more specifically stresses the utility of this graphical interpretation. On the computational side, the graphic interpretation is used to adapt the notion of an Evans function to an Evans--Krein function. The new generalization allows one to calculate the Krein signature in a way that is easy to incorporate into existing simulation capabilities that are already capable of evaluating an Evans function. This is in contrast to the traditional Evans function which cannot generally be used to directly deduce the Krein signature. In addition to this computational utility, the graphical interpretation of the Krein signature has nice theoretical properties as demonstrated by a set of proofs associated with index theorems for linearized Hamiltonians and includes relations to the well-known Vakhitov--Kolokolov criterion. PUBLICATION ABSTRACT