2×2 Matrix & Eigenvectors
This interactive simulator explores 2×2 Matrix & Eigenvectors in Math Visualization. Grid deformation under M; real λ eigen-direction arrows. Use the controls to change the scenario; watch the visualization and any graphs or readouts to connect the model with lectures, labs, and homework.
Who it's for: Best once you already know the basic definitions and want to build intuition. Typical context: Math Visualization.
Key terms
- matrix
- eigenvectors
- eigen 2x2 grid
- math
- visualization
How it works
A **linear map** **(x,y) ↦ (ax+by, cx+dy)** sends a **square grid** to a **parallelogram lattice**. **Eigenvectors** (when **λ** are **real**) lie along directions that are **only scaled** — the **right** panel overlays **two** eigen-direction **arrows** from the origin when **discriminant** **≥ 0**. **Complex** **λ** means **no** real eigen-direction pair in **ℝ²** (rotation–scale mix); the **grid** still **deforms** nicely.
Key equations
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