Matrix and linear transformation
One 2×2 matrix carries the plane by its two column vectors, and the same matrix is read again as signed area and as the order of composition.
Linear transformations
8 pieces about this concept, across works, topic guides, and exam visualizations.
Topics
Works
Linear transformation grid
A 2×2 matrix acts on the plane grid, and the figure shows shear together with vertical scaling.
Affine transformation pattern
Affine maps that combine translation, rotation, and scaling, iterated on a pattern.
Rotation and scaling, composed
The matrix product of repeated rotation and uniform scaling, and the spirals and logarithmic spirals it generates.
Iterated affine fractal
An iterated function system (IFS) iterates several affine maps and generates a self-similar fractal.
Eigenvectors and stretch factors
Switch among standard 2×2 matrices and see that an eigenvector's line still maps to itself, with the stretch set by the eigenvalue.
Exam visualizations
Rotation and reflection matrices
112 GSAT Mathematics A, Multiple select 11: compare images, inverses, and compositions of rotation and reflection matrices.
Equilateral triangle on three concentric circles
2025 AMC 12B, Problem #25 turns the radius-2 circle 60° about a vertex so that it is internally tangent to the outer circle, and the squared side is 7.