Linear transformation visualizer
Type a 2×2 matrix and watch it transform the plane: basis vectors, the determinant as area, and the eigenvectors.
Result
A = [2 1 / 1 2]
A mix of stretching and turning — read the determinant and eigenvalues to see how much of each.
How is this calculated?
Using the tool
Type a 2×2 matrix and watch what it does to the plane: where the basis vectors land, how the unit square stretches into a parallelogram (that area is the determinant), and which directions refuse to turn — the eigenvectors. Scrub the morph slider to see the transformation happen.
The math
A matrix is a recipe for moving the whole plane at once, and its columns spell it out: column 1 is where î lands, column 2 is where ĵ lands — every other vector follows by linearity. The determinant is the area of the parallelogram the unit square becomes: 2 means areas double, negative means the plane got flipped, zero means it was squashed flat onto a line. Eigenvectors are the directions the matrix cannot turn — vectors on those lines only stretch by their eigenvalue λ, found by solving det(A − λI) = 0, a quadratic for a 2×2. Rotations have no real eigenvectors (every direction turns), shears have exactly one, and symmetric matrices always have two at right angles.
New to the math? Learn the concept: Higher dimensions, made visual