Matrix Transformations

2×2 matrices as deformations of the plane

A 2×2 matrix A is fully determined by where it sends the basis vectors e₁ and e₂. Edit A directly or select a preset (rotation, shear, scale, reflection, projection); the unit square is drawn before and after to make the action visible. The determinant reports the signed area factor.

Presets

Matrix A

det(A) = 1.0000

|det| = area scale factor

A = \begin{bmatrix}1.00 & 0.00 \\ 0.00 & 1.00\end{bmatrix}, \quad \det A = 1.000

The dashed square is the unit square; the filled region is its image. e\u2081 is purple, e\u2082 is gold. Determinant is the signed area factor.

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