Linear Algebra World

Explore linear algebra through interactive matrix computations, step-by-step algorithms and a structured learning pathway. Available on iPhone, iPad and Mac.

Linear Algebra World (LAW) presents linear algebra in a way that is accessible yet rigorous. It is designed for students of engineering, mathematics, data science and related fields, and may also serve as a visual presentation tool for instructors.

The app combines three roles: • matrix calculator • interactive algorithm step visualizer • carefully designed learning pathway through linear algebra

Our goal is to present linear algebra as a coherent system built on a small set of axioms. Definitions are separated from consequences, logical dependencies are made explicit, and notation is kept minimal to reduce cognitive load.

Visual tools are used extensively—even for abstract topics such as the four fundamental subspaces—so that geometric intuition and algebraic reasoning reinforce one another.

The curriculum begins with vectors as coordinates and matrices as collections of vectors, and currently covers topics through QR factorization. Upcoming additions include OLS, eigendecomposition, SVD, and PCA.

This app builds on our earlier Matrix Solver Step by Step, a highly rated matrix computation app used by students for several years. LAW adds a structured curriculum along with LaTeX import and export.

LAW is designed for serious learners who want to understand the structure behind the computations. For quick step-by-step matrix calculations, Matrix Solver Step by Step may be the more direct tool.

Your constructive feedback is essential to the continued refinement of the app.