The quadratic eigenvalue problem (QEP) is not usually covered in introductory linear algebra or numerical methods courses. Even advanced linear algebra texts, such as Gantmacher [1], covered it only in later chapters. Since the 1960s, however, applications of the QEP to the analysis of vibrations in airfoils and other structures have led to increased theoretical interest in the QEP. This, coupled with the improved methods and error analysis in other areas of numerical linear algebra, has led to improved methods for the QEP. In turn, papers summarizing these advances have appeared [2].

In the same vein, this paper presents the highlights of these results in the context of electric power systems. The theoretical discussions in this paper use, for the most part, the approach and notation found in Tisseur and Meerbergen’s paper [2]. In the discussions of applications, however, different problems are presented to show how the theory is used. These problems include assessing the stability of a power system when significant components are removed or added because of maintenance or expansion, as well as estimating the state of the system using noisy or incomplete data. The concept of pseudospectrum [3] is shown to be useful in the latter problem.

The parts of this paper dealing with applications are well written, but the theoretical sections do not flow smoothly from topic to topic, and some definitions of notation are missing. The reader, however, can easily resolve these confusing parts by referring to the items in the extensive bibliography.