A geometric view on 2x2 matrices: how scaling and rotation combine, how eigencircles encode that behaviour, and how eigenvalues and eigenvectors can be read from the construction.
The eigencircle approach rewrites a linear transformation in terms of the pair \((s,\theta)\): a scaling factor and a rotation angle. Looking at the full set of such pairs produces a circle that captures the geometry of the matrix.
This local version is now structured as a compact overview page, a readable book view, and a separate figures page for the interactive applet and derived plots.
Instead of treating eigenvalues as purely algebraic output, the eigencircle view gives a direct visual interpretation of how a matrix acts on vectors across the plane.
That makes the relationship between vectors, images, rotation, scaling, and special directions much easier to inspect.