Exploring Matrices
Visual tools for exploring the world of 2x2 matrices.
Matrix Space
Matrix Space Explorer
Explore the relationships between over 2000 integer matrices. Sort them by properties including trace, determinant, condition number, and many more, to uncover hidden geometric patterns.
Linear Transformations
Transformation Explorer
Visualise how a 2×2 matrix transforms 2D space. Drag points, lines, and shapes to discover how they are transformed, either once or multiple times. Find invariant lines, and explore how transformations change length and area.
Linear Dynamical Systems
Sources, Sinks, and Saddles
2x2 matrices can be used to define a dynamical system (equivalent to a pair of linear Coupled Differential Equations). Explore the different types of behaviour by seeing trails or animated movements.