iMath: Digital Images Modeled with Matrices

Abstract

This paper arms today's teachers of mathematics with a response to the age-old question, "What are matrices used for anyway?" Today's students spend much of their life consuming and producing digital media. Many of these students can read images and edit digital photographs with ease. We aim to capture student's interest in mathematics by showing how the images on computer screens, tablets, and smartphones are simply matrices of numbers and each color can be represented with just three numbers. Students gain both a new appreciation for color and for mathematics when learning to see color this way. We show how addition of colors can be thought of as addition of matrices and provide examples of numerical color addition in various color models. Armed with these simple ideas of how matrices underpin digital imagery, teachers can motivate students of the digital age to learn more mathematics.