Linear Transformation Visualizer

Visualize the effects of matrix transformations on 2D shapes with animations

Overview

The Linear Transformation Visualizer provides an interactive way to see how 2×2 matrices transform 2D space. Watch shapes and coordinate grids morph in real-time as you apply rotations, scalings, shears, reflections, and custom transformations with smooth animations that reveal the geometric meaning of matrix multiplication.

Tips

  1. Watch the Grid Deformation: The coordinate grid shows how the transformation warps space - straight lines stay straight (that’s what makes it linear), and the grid pattern reveals the nature of the transformation.

  2. Start with Preset Transformations: Use the built-in rotation, scaling, shear, and reflection matrices to understand common transformations before creating your own custom matrices.

  3. Observe the Matrix Columns: The columns of your transformation matrix show exactly where the standard basis vectors (1,0) and (0,1) end up after the transformation.

  4. Experiment with Composition: Apply multiple transformations in sequence to see how they combine - remember that order matters (rotating then scaling gives different results than scaling then rotating).

  5. Try Different Shapes: Apply transformations to squares, circles, and triangles to see how different properties are preserved or changed by each type of transformation.