A Problem-Centered Approach to Canonical Matrix Forms

This article outlines a problem-centered approach to the topic of canonical matrix forms in a second linear algebra course. In this approach, abstract theory, including such topics as eigenvalues, generalized eigenspaces, invariant subspaces, independent subspaces, nilpotency, and cyclic spaces, is developed in response to the patterns discovered in studying similarity classes of square matrices, rather than as a disconnected prerequisite to this topic. Furthermore, the subtopics involved afford an opportunity to highlight many common mathematical problem-solving techniques and philosophies.