The Linear Algebra Calculator 2.0
“Linear problems are number one in all of science!” — Gilbert Strang
It started five years ago, when a new maths syllabus (or math syllabus ;) I won’t judge) required my high-school teacher, Mrs B, to introduce her class to the mysterious world of matrices: $$\begin{bmatrix}1 & 0 \\ 0 & 1\end{bmatrix}.$$ As an eleventh-grader, I had just learned a new thing called Python. As a school project, I made the Linear Algebra Calculator, a small Tkinter application that could perform matrix calculations and visualise the transformations represented by \(2\times 2\) matrices.
Mrs B was delighted and used the app across several lessons, experimenting with matrices and showing her students what the arrays of numbers actually did.
This week, I rediscovered the original script. I gave it to GPT-5.6 Sol in Codex, described what I wanted it to become, and let the agents get to work.
The result is the Linear Algebra Calculator 2.0, if you are a teacher looking to teach a class in linear algebra when school starts, I hope this helps!
What it does
LAC 2.0 is a modern, easy-to-use tool for teaching linear algebra through computation and geometry.
It performs the standard matrix operations one expects from a calculator, including addition, multiplication and diagonalisation. Its real strength, however, is its interactive visualisations. You can watch a singular matrix collapse the plane onto a line, see why eigenspaces are preserved by a transformation, and give the algebraic calculations their crucial geometric intuitions. As Strang puts it:
“Matrices act. They don’t just sit there!"
How it was built
This week, I gave Codex the original LAC script and a goal: transform this high school project into a polished, modern classroom application.
Codex inspected the existing program, proposed a modernisation plan, and began implementing it. The first run already produced a (really good!) working product. From there, I directed further iterations: refining UI, adding new maths functionality, etc, based on my vision for the LAC. Codex was able to open an internal browser, and test the web app on its own, which was remarkable and saved me so much effort.
Apart from the original script, the new application was built entirely by GPT-5.6 Sol Ultra through Codex in this week.
What I learned
Maths, and in general STEM subject teachers around the world face growing shortages of time, support and high-quality resources tailored to their students. Yet a proper understanding of mathematics and numeracy remains foundational to almost every area of science and technology.
The original LAC existed because one particular teacher (who, if I may add, was adored by all her students), wanted a better way to introduce matrices for her class. Until recently, creating a custom interactive application for that need would have required considerable programming experience and development time.
With Codex, if building a web application can be done within a few prompts, why should teachers be limited to worksheets and slides inherited from old textbooks? They could instead create interactive resources adapted to their syllabus, teaching style and students, while Codex handles much of the implementation in the background.
What comes next
For LAC 2.0, the next step is to introduce visualisations for more advanced topics, including QR factorisation and low-rank approximation.
The broader goal is to build an education-specific system that helps teachers create their own interactive classroom tools without any software developers. A teacher should be able to describe the concept their students are struggling with and receive a resource they can immediately explore, adapt and use, making their lives a lot less stressful.
Five years ago, LAC was built for one teacher. LAC 2.0 gives me this idea: But every teacher could build their own?
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