Visualisation of matrix product: Using light to clarify an abstract mathematical concept

TL;DR

This paper introduces an experimental activity using polarized light and Jones calculus to visually demonstrate the noncommutative property of matrix multiplication, making an abstract concept more accessible for students.

Contribution

It presents a novel, hands-on teaching method that leverages light polarization to clarify the noncommutativity of matrix products for educational purposes.

Findings

The activity effectively demonstrates matrix noncommutativity visually.

It aids in teaching matrices in physics and mathematics.

The method enhances understanding of abstract mathematical concepts.

Abstract

Teaching the noncommutativity of the product of matrices to high school or college level students is a difficult task when approached from a purely formal perspective. The aim of this paper is to present a simple experimental activity for teaching the noncommutativity of the matrix product, based on the Jones calculus, a mathematical formalism for describing polarised light by means of matrices and vectors. This activity can also be useful to introduce students to the use of matrices in physics, and to illustrate how abstract mathematics can become a powerful tool to help us explain and describe the real world.