PPolySim OS

Eigenvector Visualizer

A matrix warps space, but some directions only stretch — never turn. Those are its eigenvectors, and how much they stretch are its eigenvalues.

Eigenvector VisualizerLive

Controls

A matrix warps the unit circle into an ellipse. Eigenvectors are the special directions that only stretch — never rotate — by their eigenvalue.

Presets

▶ Run in Python

Data Inspector

det3.00
trace4.00
λ₁3.00
λ₂1.00

Governing equation

Reading this result: Symmetric matrix (b = c): its eigenvectors meet at right angles, so the ellipse axes line up exactly with the green and pink lines.

Runs locally in your browser — free forever. Scale to the cloud when reality gets heavy.

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How it works

This visualizes a 2×2 linear transformation by morphing the unit circle into an ellipse, and overlays the eigenvectors — the directions the matrix leaves unrotated — with their eigenvalues computed from the trace and determinant. The heart of linear algebra, PCA, and stability analysis.

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Frequently asked questions

Is this eigenvectors eigenvalues tool really free?
Yes. Eigenvector Visualizer runs entirely in your browser using your device's own compute, so local use is free forever. You only pay Compute Tokens if you scale a job to the cloud.
Do I need to install anything?
No. Everything runs client-side in a modern browser — no downloads, no license, no account required to start.
Can I save or share my simulation?
Create a free account to save projects, and use a shareable embed or minted DOI to publish a live, interactive version anywhere.
How accurate are the results?
The solver uses established numerical methods, but results are for research and educational purposes and should be validated against experiment or professional review before you rely on them.