Linear Transformation Playground
A 2×2 matrix is a machine that moves every point of the plane, and the best way to understand one is to watch it act. This playground shows the plane’s grid together with the basis vectors î and ĵ; set the four matrix entries and the grid smoothly morphs from the identity to your transformation. Shears, rotations, scalings and reflections all become visible, the determinant is displayed live as the (signed) area of the unit square’s image, and presets show the classic transformations.
Runs 100% in your browser — simulations are computed locally on your device.
Read the full guide to this tool
Notes
- The columns of the matrix are simply where î and ĵ land — everything else follows by linearity.
- The determinant is the signed area of the transformed unit square: 0 flattens the plane, negative flips its orientation.
- Composing transformations multiplies their matrices, in right-to-left order.
- Runs 100% in your browser — simulations are computed locally on your device.
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