Eigenvalues of nonsingular matrices and combinatorial applications

Abstract

The purpose of this orticle is to present a result about eigenvalues of nonsingular matrices and to observe that this result implies a theorem of this author on combinatorial desiqns as well as other combinatorial results. The material presented herein lends itself well for use as an ilustration of some nontrivial applications in a first course in Linear Algebra; these applications may be mentioned right after the concepts of eigenvalue and eigenvector have been defined.