Immersive Math: A Free Linear Algebra Textbook Built Around Interactive Figures

Written by J. Ström, K. Åström, and T. Akenine-Möller, Immersive Linear Algebra is a web-based textbook that pairs a standard undergraduate curriculum with figures readers can manipulate directly in the browser. Rather than static diagrams, each illustration responds to interaction, letting students see how operations like vector addition, dot and cross products, and matrix transformations behave as inputs change. The authors bill it as the first linear algebra book with fully interactive figures.

The content follows a conventional progression: a preliminary chapter on notation and prerequisite math, then vectors and their arithmetic, the dot product, the cross product in three dimensions, systems of linear equations, and finally matrices and their properties, including the determinant and the principle of linearity. The interactive approach is the differentiator — the goal is to build geometric intuition for concepts that are often taught purely symbolically.

For a technical audience, the appeal is practical: linear algebra is foundational to graphics, simulation, and machine learning, and a freely accessible resource that emphasizes visual intuition lowers the barrier to (re)learning the material. Two of the authors are known in the computer graphics community, which is reflected in the book’s emphasis on geometric interpretation.