Matrix Visualizer

Interactive visualizer for 2×2 and 3×3 linear transformations — a single self-contained HTML file, no dependencies, no build step.

Live demo →

Features

• Animated transformations — two animation paths:
  • blend: M(t) = (1−t)·I + t·M, which keeps every eigendirection of M invariant for all t, so you can watch the grid slide along the eigenlines;
  • rotate · scale · rotate: the motion is decomposed into its SVD steps M = U·Σ·Vᵀ and played as rotation → axis scaling → rotation (in 3D via axis–angle interpolation of U and Vᵀ).
• 2D mode — draggable basis vectors (î, ĵ), transformed grid, unit square with live determinant, eigenlines with eigenvalue labels, unit circle → ellipse (singular values), axis ticks.
• 3D mode — orbit camera, transformed lattice, unit cube → parallelepiped, eigenlines and eigenplanes (for repeated eigenvalues), unit sphere → ellipsoid.
• Full analysis panel — determinant, trace, rank, eigenvalues (including complex pairs), eigenvectors, singular values, characteristic polynomial, and automatic classification (rotation, shear, reflection, projection, symmetric, singular, …).
• Decompositions — diagonalization M = P·D·P⁻¹ when possible, otherwise the Jordan normal form M = P·J·P⁻¹ with generalized eigenvectors (all 3×3 block structures supported), the real canonical form M = P·C·P⁻¹ for complex eigenvalues, the full SVD M = U·Σ·Vᵀ, and the inverse M⁻¹.
• Probe vector (2D) — double-click anywhere to drop an input vector v and watch M(t)·v move with live coordinates; drag its tip to reposition, double-click it to remove.
• Quick operations — one-click Mᵀ, M⁻¹, −M, M²; ⇧-click any preset to compose it onto the current matrix.
• Shareable URLs — the matrix and mode are encoded in the URL hash (#3d:…), so any state can be shared as a link.
• 24 presets across both modes: rotations, shears, reflections, projections, spirals, singular and symmetric matrices.

Usage

Open index.html in a browser. That's it.

Interaction	Effect
Drag î / ĵ tips (2D)	Edit the matrix directly (⇧ snaps to 0.5)
Double-click (2D)	Place / remove a probe vector
⇧-click a preset	Compose it onto the current matrix
Drag (3D)	Orbit the camera
Scroll	Zoom
Space	Play / pause the animation

All the math (eigendecomposition via analytic quadratic/cubic solvers, Jordan chains, complex eigenvectors, SVD values) is implemented from scratch in the single file.