First Advisor
Dr. Jeffery Ovall
Date of Award
Summer 8-2025
Document Type
Thesis
Degree Name
Bachelor of Science (B.S.) in Mathematics and University Honors
Department
Mathematics
Language
English
Subjects
Linear Algebra, Matrix R, Color Space, Primary Colors, Modelling, Colorimetry
Abstract
This thesis surveys the mathematical grounding of linear algebraic models of color. It aims to build from the ground up the framework by which additive color is broadly understood in the digital age. Primarily building on the work of Jozef Cohen, Eric Dubois, David H. Krantz, and Günter Wyszecki, it aims to chart the construction of a model of color that underpins most modern understandings of color. While the construction is certainly established in colorimetric circles, the construction is, in the thesis author’s opinion, either obtuse or non-rigorous. Ideally, this thesis serves to make the construction accessible to an audience with a background in linear algebra. Secondary goals of this thesis include dispelling misconceptions around the role of primary colors and highlighting potential extensions to the standard linear algebraic model to encourage further research.
The construction of the linear algebraic model begins by defining spectral power distribution and color spaces as commutative semi-groups [(𝒫,+) and (𝒞,⊕)] which can be embedded in vector spaces (𝒜 and 𝒬). Some properties of these vector spaces are then discussed, before moving onto using discrete approximations to implement a linear transformation between the spaces. Finally, Cohen’s Matrix 𝐑 technique is used to rigorously define representatives for color sensation equivalency classes (the suite of all color sensations that look like the same color).
Recommended Citation
Martin, Isaac, "An Exploration of the Structure of the Linear Algebraic Model of Color" (2025). University Honors Theses. Paper 1759.