On Springs and Matrices

Abstract

It is shown that the mechanical behavior of an elementary two-spring structure can be used as a direct realization of practically all those concepts of matrix analysis that are usually taught in undergraduate engineering studies: positiveness, symmetry, eigenvalues (vectors) with their orthogonality and extreme properties, invariants, similarity, and so on. The interaction between pure mathematical concepts and a well known physical example creates an associative learning process that helps students to grasp abstract ideas and naturally generalizes scientific concepts from their intuitive level on the physical space to their abstract n-dimensional framework. It is therefore proposed that matrix (tensor) algebra should be explored as an inherent part of the basic course in mechanics.