Apply a matrix transformation to a vector and visualise the mapped coordinates.
A linear transformation T(x) = Ax maps a vector x through the matrix A. Each output component is the dot product of the corresponding row of A with x. Common 2D examples include rotations, reflections, and scaling. The matrix A provided here (default) is a 90° counter-clockwise rotation.
Linear Map
(Ax)ᵢ = Σⱼ Aᵢⱼ xⱼ
Any linear transformation: rotations, reflections, scaling, shearing, projections, and compositions of these. Non-linear transformations (like translation) require augmented matrices.
Only if A is an orthogonal matrix (AᵀA = I). Orthogonal matrices represent rotations and reflections which preserve lengths and angles.