This is the summary of a presentation given at the Joint Mathematics Meetings, January 10-13, 1996, Orlando, Florida.

Linear maps in inner product spaces are those maps which change angles or lengths of vectors. Eigenvectors are special vectors in a sense that carry the same angles or carry opposite angles under linear maps. Eigenvectors are important concepts in Linear Algebra. But beginning linear algebra students lack experience with linear operators and may find the topic of eigenvectors difficult. However, with an analytic geometry and calculus background students have no difficulty understanding symmetry. The eigenvector belonging to a eigenvalue 1 can be visioned as the axis of the symmetry of a geometrical figure in Euclidean 2-space (as the axis of the reflection) or 3-space (as the axis of the rotation). We will discover this with working on regular n-gons in a plane or a tetrahedron in a space.

Saeja Oh Kim, University of Massachusetts at Dartmouth